Finite Fields and Their Applications

Total Page:16

File Type:pdf, Size:1020Kb

Finite Fields and Their Applications FINITE FIELDS AND THEIR APPLICATIONS AUTHOR INFORMATION PACK TABLE OF CONTENTS XXX . • Description p.1 • Audience p.1 • Impact Factor p.1 • Abstracting and Indexing p.2 • Editorial Board p.2 • Guide for Authors p.4 ISSN: 1071-5797 DESCRIPTION . Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field- related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm. Finite Fields and Their Applications is published four times per year and maintains very strict refereeing standards, accepting only those papers which receive excellent referee reports.This journal has an Open Archive. All published items, including research articles, have unrestricted access and will remain permanently free to read and download 48 months after publication. All papers in the Archive are subject to Elsevier's user license. AUDIENCE . Research mathematicians, Applied research mathematicians, Defence agencies IMPACT FACTOR . 2020: 1.773 © Clarivate Analytics Journal Citation Reports 2021 AUTHOR INFORMATION PACK 25 Sep 2021 www.elsevier.com/locate/ffa 1 ABSTRACTING AND INDEXING . Scopus ACM Guide to Computing Literature CompuMath Citation Index Current Contents - Physical, Chemical & Earth Sciences Science Citation Index Current Contents Zentralblatt MATH EDITORIAL BOARD . Editor-in-Chief Gary L. Mullen, The Pennsylvania State University, University Park, United States of America Editorial Board Anne Canteaut, National Research Institute for Computing and Automation, BP 105, 78153, Le Chesnay, France Pascale Charpin, Inria Research Centre of Paris, 75589, Paris, France Stephen D. Cohen, University of Glasgow School of Mathematics and Statistics, University Gardens, G12 8QW, Glasgow, United Kingdom Michael Fried, University of California Irvine Department of Mathematics, 540J Rowland Hall, CA 92697-3875, Irvine, California, United States of America Massimo Giulietti, Università degli Studi di Perugia, Dipartimento di Matematica e Informatica, Via Vanvitelli 1, 06123, Perugia, Italy James W.E. Hirschfeld, University of Sussex Department of Mathematics, BN1 9RF, Brighton, United Kingdom Xiang-dong Hou, University of South Florida Department of Mathematics and Statistics, 4202 E. Fowler Avenue, FL 33620, Tampa, Florida, United States of America William Cary Huffman, Loyola University Chicago Department of Mathematics and Statistics, Damen Hall Suite 350, 6525 North Sheridan Road, IL 60626, Chicago, Illinois, United States of America Dieter Jungnickel, University of Augsburg Institute of Mathematics, Universitätstr.8, 86135, Augsburg, Germany Neal Koblitz, University of Washington Department of Mathematics, Box 354350, Padelford C-445, 98195-4350, Seattle, Washington, United States of America Michel Lavrauw, Sabanci University, 34956, İstanbul, Turkey Rudolf Lidl, University of Tasmania Mathematics Newnham Campus, Newnham Drive, P.O Box 1214, Launceston, TAS 7250, Tasmania, Australia Gary McGuire, University College Dublin School of Mathematics and Statistics, Belfield, Dublin, Ireland Harald Niederreiter, Johannes Kepler University Linz, Altenbergerstr. 69, 4040, Linz, Austria Andrew M. Odlyzko, University of Minnesota Twin Cities, 55455, Minneapolis, Minnesota, United States of America Daniel Panario, Carleton University School of Mathematics and Statistics, 1125 Colonel By Drive, Ottawa, K1S 5B6, Ontario, Canada Vera Pless, University of Illinois at Chicago, 60607-7101, Chicago, Illinois, United States of America Olga Polverino, University of Campania Luigi Vanvitelli Department of Mathematics and Physics, Viale Lincoln 5, 81100, Caserta, Italy Sergey Rybakov, HSE Laboratory of Algebraic Geometry and its Applications, 6 Usacheva Str., 119048, Moscow, Russian Federation Shojiro Sakata, University of Electrocommunications Faculty of Informatics and Engineering Graduate School of Informatics and Engineering, Chofu-ga-oka 1-5-1, 182-8585, Chofu, Japan Peter Jau-Shyong Shiue, University of Nevada Las Vegas Department of Mathematical Sciences, NV 89154-4020, Las Vegas, Nevada, United States of America Igor Shparlinski, University of New South Wales Department of Pure Mathematics, Sydney, 2052, New South Wales, Australia Neil Sloane, The OEIS Foundation Inc, 08904, Highland Park, New Jersey, United States of America Leo Storme, Ghent University Department of Mathematics Algebra and Geometry, Krijgslaan 281, 9000, Gent, Belgium Daqing Wan, University of California Irvine Department of Mathematics, 540J Rowland Hall, CA 92697-3875, Irvine, California, United States of America Zhe-Xian Wan, Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences, 100190, Beijing, China Qiang (Steven) Wang, Carleton University School of Mathematics and Statistics, 1125 Colonel By Drive, Ottawa, K1S 5B6, Ontario, Canada Arne Winterhof, Johann Radon Institute for Computational and Applied Mathematics, 4040, Linz, Austria Chaoping Xing, Shanghai Jiao Tong University School of Electronic Information and Electrical Engineering, Shanghai, China AUTHOR INFORMATION PACK 25 Sep 2021 www.elsevier.com/locate/ffa 2 Publisher Giovanni Raneri, Elsevier, AUTHOR INFORMATION PACK 25 Sep 2021 www.elsevier.com/locate/ffa 3 GUIDE FOR AUTHORS . Your Paper Your Way We now differentiate between the requirements for new and revised submissions. You may choose to submit your manuscript as a single Word or PDF file to be used in the refereeing process. Only when your paper is at the revision stage, will you be requested to put your paper in to a 'correct format' for acceptance and provide the items required for the publication of your article. To find out more, please visit the Preparation section below. INTRODUCTION Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm. Finite Fields and Their Applications is published four times per year and maintains very strict refereeing standards, accepting only those papers which receive excellent referee reports. Contact details for submission Online submission. Authors are encouraged to submit their papers electronically using the Elsevier electronic submission tool located at https://www.editorialmanager.com/ffa/default.aspx and click on the "Submit online to this journal" link located under "Journal Services." Submission checklist You can use this list to carry out a final check of your submission before you send it to the journal for review. Please check the relevant section in this Guide for Authors for more details. Ensure that the following items are present: One author has been designated as the corresponding author with contact details: • E-mail address • Full postal address All necessary files have been uploaded: Manuscript: • Include keywords • All figures (include relevant captions) • All tables (including titles, description, footnotes) • Ensure all figure and table citations in the text match the files provided • Indicate clearly if color should be used for any figures in print Graphical Abstracts / Highlights files (where applicable) Supplemental files (where applicable) Further considerations • Manuscript has been 'spell checked' and 'grammar checked' • All references mentioned in the Reference List are cited in the text, and vice versa • Permission has been obtained for use of copyrighted material from other sources (including
Recommended publications
  • IEEE Information Theory Society Newsletter
    IEEE Information Theory Society Newsletter Vol. 70, No. 2, June 2020 EDITOR: Salim El Rouayheb ISSN 1059-2362 President’s Column Aylin Yener The last time I wrote to you was in a differ- to ensure timely publication of outstanding ent lifetime. In the past three months, we papers that show the impact of information have witnessed a pandemic with devastating theoretic thinking in fields such as learning, impact that had cost lives and disrupted life quantum, security and others. I hope that you as we know it, in every way we can imagine. will find this new member benefit a valuable The pandemic is still far from under control in resource for your research and professional much of the world, and we do not have a date development. that we can expect to have some normalcy; of course everyone is hoping for sooner than We are now preparing to launch our new later. I still feel like I entered the twilight zone, magazine IEEE BITS. Like JSAIT, this new but have reluctantly accepted that this is not publication is also several years in the making a bad dream as I originally thought, but is the with diligent efforts of the magazine commit- new normal (at least for sometime). In dif- tee under the leadership of Christina Fragou- ficult times like these, humanity is often at its li. The magazine will start publishing in 2021 best (of course there are always exceptions); under the leadership of Rob Calderbank. We one quickly converges to what really matters thank Prof. Fragouli and the committee for in life and all of a sudden set backs that seemed monumen- spearheading this effort and Prof.
    [Show full text]
  • Editorial Philippe Gaborit Jon-Lark Kim
    Int. J. Information and Coding Theory, Vol. 1, No. 3, 2010 245 Editorial Philippe Gaborit XLIM-DMI, University of Limoges, 123, Avenue Albert Thomas, 87000 Limoges, France E-mail: [email protected] Jon-Lark Kim* Department of Mathematics, University of Louisville, 328 Natural Sciences Building, Louisville, KY 40292, USA E-mail: [email protected] *Corresponding guest editor Patrick Solé Telecom ParisTech, Dept COMELEC, 46, rue Barrault, 75013 Paris, France E-mail: [email protected] Isaac Woungang Department of Computer Science, Ryerson University, Toronto, Ontario M5B 2K3, Canada E-mail: [email protected] Biographical notes: Philippe Gaborit received a PhD from the University of Bordeaux in 1997. After a two years post-doc with Vera Pless in Chicago, he became an Associate Professor at the University of Limoges in 1999 and a Professor in 2008. His main research interests are cryptography, coding theory and security. Jon-Lark Kim received his BS in Mathematics from POSTECH, Pohang, Korea, in 1993, an MS in Mathematics from Seoul National University, Korea, in 1997 and a PhD in Mathematics from the University of Illinois at Chicago, in 2002 under the guidance of Prof. Vera Pless. From 2002 to 2005, he was with the Department of Mathematics at the University of Nebraska – Lincoln as a Research Assistant Professor. Since 2005, he has been an Assistant Professor in the Department of Mathematics at the University of Louisville, Louisville, KY. He was awarded a 2004 Kirkman Medal of the Institute of Combinatorics Copyright © 2010 Inderscience Enterprises Ltd. 246 P. Gaborit et al. and its Applications.
    [Show full text]
  • Fundamentals of Error-Correcting Codes W
    Cambridge University Press 978-0-521-13170-4 - Fundamentals of Error-Correcting Codes W. Cary Huffman and Vera Pless Frontmatter More information Fundamentals of Error-Correcting Codes Fundamentals of Error-Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint. As well as covering classical topics, much coverage is included of recent techniques that until now could only be found in special- ist journals and book publications. Numerous exercises and examples and an accessible writing style make this a lucid and effective introduction to coding theory for advanced undergraduate and graduate students, researchers and engineers, whether approaching the subject from a mathematical, engineering, or computer science background. Professor W. Cary Huffman graduated with a PhD in mathematics from the California Institute of Technology in 1974. He taught at Dartmouth College and Union College until he joined the Department of Mathematics and Statistics at Loyola in 1978, serving as chair of the department from 1986 through 1992. He is an author of approximately 40 research papers in finite group theory, combinatorics, and coding theory, which have appeared in journals such as the Journal of Algebra, IEEE Transactions on Information Theory, and the Journal of Combinatorial Theory. Professor Vera Pless was an undergraduate at the University of Chicago and received her PhD from Northwestern in 1957. After ten years at the Air Force Cambridge Research Laboratory, she spent a few years at MIT’s project MAC. She joined the University of Illinois-Chicago’s Department of Mathematics, Statistics, and Computer Science as a full professor in 1975 and has been there ever since.
    [Show full text]
  • Program of the Sessions – Columbus, OH, Friday, September 21 (Cont’D.)
    Program of the Sessions Columbus, Ohio, September 21–23, 2001 2:00PM New lower bounds on the maximum number of Friday, September 21 (6) mutually orthogonal Steiner triple systems. Preliminary report. Meeting Registration Jeff Dinitz*, University of Vermont, and Peter Dukes, Calif. Institute of Technology (969-05-233) 12:30 PM –4:30PM MW 154, Mathematics Tower (MW) 2:30PM On abelian relative difference sets which are (7) extensions of diffrence sets with classical AMS Exhibit and Book Sale parameters. Preliminary report. Nobuo Nobu Nakagawa, Naka, Department of 12:30 PM –4:30PM MW 724, Mathematics Tower (MW) Mathematics Faculty of Science and Technology (969-05-66) Special Session on Algebraic Cycles, Algebraic 3:00PM Higher Weights and Nonbinary Self-Dual Codes. Geometry, I (8) Steven T Dougherty, University of Scranton, and Aaron Gulliver*, University of Victoria (969-94-220) 1:30 PM –5:15PM UH 0151, UniversityHall (UH) 3:30PM A technique for constructing non-embeddable (9) quasi-residual designs. Organizer: RoyJoshua , Ohio State University YuryJ. Ionin *andKirsten Mackenzie-Fleming, 1:30PM Equivariant Todd Classes for Toric Varieties. Central Michigan University (969-05-246) (1) Jean-Luc Brylinski, Penn State University, and Bin 4:00PM An Existence Theorem for Group Divisible 2-Designs Zhang*, SUNY at Stony Brook (969-14-131) (10) of Large Order. 2:30PM Combinatorics of the Toric Hilbert Scheme. Hedvig Mohacsy*andDijen K Ray-Chaudhuri,The (2) Rekha R Thomas*, University of washington, and Ohio State University (969-05-250) , Institute for Advanced Study Diane Maclagan 4:30PM Extremal problems under dimension constraints. (969-05-185) (11) Preliminary report.
    [Show full text]
  • Editorial Philippe Gaborit Jon-Lark Kim* Patrick Solé Isaac Woungang
    Int. J. Information and Coding Theory, Vol. 1, No. 2, 2010 129 Editorial Philippe Gaborit XLIM-DMI, University of Limoges, 123, Avenue Albert Thomas, 87000 Limoges, France E-mail: [email protected] Jon-Lark Kim* Department of Mathematics, University of Louisville, 328 Natural Sciences Building, Louisville, KY 40292, USA E-mail: [email protected] *Corresponding guest editor Patrick Solé Telecom ParisTech, Dept COMELEC, 46, rue Barrault, 75013 Paris, France E-mail: [email protected] Isaac Woungang Department of Computer Science, Ryerson University, Toronto, Ontario M5B 2K3, Canada E-mail: [email protected] Biographical notes: Philippe Gaborit received a PhD from the University of Bordeaux in 1997. After a two years post-doc with Vera Pless in Chicago, he became an Associate Professor at the University of Limoges in 1999 and a Professor in 2008. His main research interests are cryptography, coding theory and security. Jon-Lark Kim received his BS in Mathematics from POSTECH, Pohang, Korea, in 1993, an MS in Mathematics from Seoul National University, Korea, in 1997 and a PhD in Mathematics from the University of Illinois at Chicago, in 2002 under the guidance of Prof. Vera Pless. From 2002 to 2005, he was with the Department of Mathematics at the University of Nebraska – Lincoln as a Research Assistant Professor. Since 2005, he has been an Assistant Professor in the Department of Mathematics at the University of Louisville, Louisville, KY. He was awarded a 2004 Kirkman Medal of the Institute of Combinatorics Copyright © 2010 Inderscience Enterprises Ltd. 130 P. Gaborit et al. and its Applications.
    [Show full text]
  • Weighted Generating Functions and Configuration Results for Type II
    Weighted Generating Functions and Configuration Results for Type II Lattices and Codes An honors thesis presented by Scott Duke Kominers to The Department of Mathematics in partial fulfillment of the requirements for the degree of Bachelor of Arts with Honors in the subject of Mathematics Harvard University Cambridge, Massachusetts March 2009 Thesis Advisor: Professor Noam D. Elkies Abstract We present an exposition of weighted theta functions, which are weighted generating functions for the norms and distribution of lattice vectors. We derive a decomposition theorem for the space of degree-d homogeneous polynomials in terms of spaces of harmonic polynomials and then prove that the weighted theta functions of Type II lattices are examples of modular forms. Our development of these results is structural, related to the infinite-dimensional representation theory of the Lie algebra sl2. We give several applications of weighted theta functions: a condition on the root systems of Type II lattices of rank 24; a proof that extremal Type II lattices yield spherical t-designs; and configuration results for extremal Type II lattices of ranks 8, 24, 32, 40, 48, 56, 72, 80, 96, and 120, one of which has not appeared previously. Then, we give a new structural development of harmonic weight enumerators—the coding- theoretic analogs of weighted theta functions—in analogy with our approach to weighted theta functions. We use the finite-dimensional representation theory of sl2 to derive a decomposition the- orem for the space of degree-d discrete homogeneous polynomials in terms of the spaces of discrete harmonic polynomials and then prove a generalized MacWilliams identity for harmonic weight enu- merators.
    [Show full text]
  • Editorial Philippe Gaborit Jon-Lark Kim
    Int. J. Information and Coding Theory, Vol. 1, No. 4, 2010 351 Editorial Philippe Gaborit XLIM-DMI, University of Limoges, 123 av. Albert Thomas, 87000 Limoges, France E-mail: [email protected] Jon-Lark Kim* Department of Mathematics, University of Louisville, 328 Natural Sciences Building, Louisville, KY 40292, USA E-mail: [email protected] *Corresponding guest editor Patrick Solé Telecom ParisTech, Department of Comelec, 46 rue Barrault, 75013 Paris, France E-mail: [email protected] Isaac Woungang Department of Computer Science, Ryerson University, Toronto, Ontario M5B 2K3, Canada E-mail: [email protected] Biographical notes: Philippe Gaborit received a PhD at the University of Bordeaux in 1997. After a two years post-doc with Vera Pless in Chicago, he became an Associate Professor at the University of Limoges in 1999, and a Professor in 2008. His main research interests are cryptography, coding theory and security. Jon-Lark Kim received the BS in Mathematics from POSTECH, Pohang, Korea, in 1993, the MS in Mathematics from Seoul National University, Korea, in 1997, and the PhD in Mathematics from the University of Illinois at Chicago, in 2002 under the guidance of Prof. Vera Pless. From 2002 to 2005, he was with the Department of Mathematics at the University of Nebraska- Lincoln as a Research Assistant Professor. Since 2005, he has been an Assistant Professor in the Department of Mathematics at the University of Louisville, Louisville, KY. He was awarded a 2004 Kirkman Medal of the Institute of Copyright © 2010 Inderscience Enterprises Ltd. 352 P. Gaborit et al. Combinatorics and its Applications.
    [Show full text]
  • Faculty List
    Faculty List Krystal Lewis MLIS, University of Illinois at University Library Urbana-Champaign Firouzeh Logan Annie Armstrong MLIS, Dominican University, MLS, University of Wisconsin–Madison MA, DePaul University Felicia Barrett Rebecca Lowery MLS, Indiana University MLIS, Dominican University, Kathryn Carpenter PhD, MA, University of Louisville MSLS, University of Illinois at H. Robert Malinowsky Urbana-Champaign MLS, University of Denver (Emeritus) Sara Blaszczak Lisa Massengale MLIS, University of Illinois at MLIS, University of Pittsburgh Urbana-Champaign Kavita Mundle Deborah Blecic MLS, Dominican University MS, University of Illinois at Urbana-Champaign Kevin O’Brien John Stephen Brantley MLS, Indiana University MLS, Indiana University, Bloomington, Cleo Pappas MA, Indiana University, Bloomington MLIS, Dominican University Mary Case Kimberly Pendell AMLS, University of Michigan, MSIS, University of Texas-Austin MA, Syracuse University , Elizabeth Pickard John M. Cullars MLS, University of Michigan MLS, Rebecca Raszewski PhD, Indiana University MLS, Drexel University Robert A. Daugherty Robert Sandusky MS, University of Illinois at Urbana-Champaign MA, Northern Illinois University, Sandra De Groote PhD, University of Illinois at Urbana-Champaign MLS, University of Western Ontario Ellen Schellhause Josephine L. Dorsch MLIS, University of Kentucky MALS, Rosary College Carol Scherrer Joan B. Fiscella MALS, Rosary College AMLS, University of Michigan, Helen F. Schmierer MA, MA, Indiana University, Bloomington PhD, University of Notre
    [Show full text]
  • Of the American Mathematical Society ABCD Springer.Com
    ISSN 0002-9920 Notices of the American Mathematical Society ABCD springer.com Highlights in Springer’s eBook Collection of the American Mathematical Society November 2009 Volume 56, Number 10 NEW NEW NEW Andrew M. Gleason (1921–2008) This book stresses applications of real Starting with basic principles, this book This accessible book offers a general analysis, detailing how its principles and provides a comprehensive classification introduction to delay differential page 1236 theory can be applied in a variety of of the various types of finite reflection equations. It is a revised version of a settings in subjects ranging from groups and describes their underlying series of lectures given at the Université Fourier series and polynomial geometric properties. Numerous Libre de Bruxelles and then at the approximation to discrete dynamical exercises at various levels of difficulty Université Joseph Fourier (Grenoble) Interview with systems and nonlinear optimization. are included. during the spring of 2003. Yuri Manin 2009. Approx. 520 p. 80 illus. 2010. XII, 172 p. 74 illus. (Universitext) 2009. XII, 204 p. (Surveys and Tutorials in (Undergraduate Texts in Mathematics) Softcover the Applied Mathematical Sciences, page 1268 Hardcover ISBN 978-0-387-79065-7 7 $49.95 Volume 3) Softcover ISBN 978-0-387-98097-3 7 $79.95 ISBN 978-0-387-74371-4 7 $39.95 Review of For access check with your librarian The Princeton Companion to Mathematics Colorado Mathematical Deformation Theory A Course in Mathematical page 1276 Olympiad R. Hartshorne , University of California, Logic for Mathematicians The First Twenty Years and Further Berkeley, CA, USA Y. I.
    [Show full text]
  • December 2007 Table of Contents
    Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Quadratic Diophantine Equations Fibonacci’s De Practica T. Andreescu , University of Dallas, Dallas, TX, USA; D. Andrica , Geometrie University Cluj-Napoca, Romania B. Hughes , Sherman Oaks, CA, USA This text treats the classical theory of quadratic diophantine Leonardo da Pisa, better known as of the American Mathematical Society equations and guides the reader through the last two decades of Fibonacci, selected the most useful parts December 2007 Volume 54, Number 11 computational techniques and progress in the area. The of Greco-Arabic geometry for the book De presentation features two basic methods to investigate and Practica Geometrie. This translation is a motivate the study of quadratic diophantine equations: the theories reconstruction of the book as the author of continued fractions and quadratic fi elds. It also discusses Pell’s judges Fibonacci wrote it, thereby equation and its generalizations, and presents some important correcting inaccuracies found in modern histories. It is a high quality quadratic diophantine equations and applications. The inclusion of translation with supplemental text to explain text that has been examples makes this book useful for both research and classroom more freely translated. A bibliography of primary and secondary settings. resources, completed by an index of names and special words is included. 2008. Approx. 250 p. 20 illus. (Springer Monographs in Mathematics) Softcover 2008. Approx. 320 p. 416 illus. (Sources and Studies in the History of ISBN 978-0-387-35156-8 7 approx. $59.95 Mathematics and Physical Sciences) Hardcover ISBN 978-0-387-72930-5 7 approx.
    [Show full text]