Associated T-designs and Automorphism Groups of Certain Linear Codes
Author: Edward Paul Shaughnessy
Publisher:
Published: 1969
Total Pages: 88
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Edward Paul Shaughnessy
Publisher:
Published: 1969
Total Pages: 88
ISBN-13:
DOWNLOAD EBOOKAuthor: Cunsheng Ding
Publisher: World Scientific
Published: 2021-12-20
Total Pages: 540
ISBN-13: 9811251347
DOWNLOAD EBOOKSince the publication of the first edition of this monograph, a generalisation of the Assmus-Mattson theorem for linear codes over finite fields has been developed, two 70-year breakthroughs and a considerable amount of other progress on t-designs from linear codes have been made. This second edition is a substantial revision and expansion of the first edition. Two new chapters and two new appendices have been added, and most chapters of the first edition have been revised.It provides a well-rounded and detailed account of t-designs from linear codes. Most chapters of this book cover the support designs of linear codes. A few chapters deal with designs obtained from linear codes in other ways. Connections among ovals, hyperovals, maximal arcs, ovoids, special functions, linear codes and designs are also investigated. This book consists of both classical and recent results on designs from linear codes.It is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications, or finite geometry. It can also be used as a textbook for postgraduates in these subject areas.Related Link(s)
Author: E. F. Assmus
Publisher: Cambridge University Press
Published: 1994-01-06
Total Pages: 366
ISBN-13: 9780521458399
DOWNLOAD EBOOKA self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.
Author: Steven Roman
Publisher: Springer Science & Business Media
Published: 1992-06-04
Total Pages: 520
ISBN-13: 9780387978123
DOWNLOAD EBOOKThis book is an introduction to information and coding theory at the graduate or advanced undergraduate level. It assumes a basic knowledge of probability and modern algebra, but is otherwise self- contained. The intent is to describe as clearly as possible the fundamental issues involved in these subjects, rather than covering all aspects in an encyclopedic fashion. The first quarter of the book is devoted to information theory, including a proof of Shannon's famous Noisy Coding Theorem. The remainder of the book is devoted to coding theory and is independent of the information theory portion of the book. After a brief discussion of general families of codes, the author discusses linear codes (including the Hamming, Golary, the Reed-Muller codes), finite fields, and cyclic codes (including the BCH, Reed-Solomon, Justesen, Goppa, and Quadratic Residue codes). An appendix reviews relevant topics from modern algebra.
Author: Derek F. Holt
Publisher: CRC Press
Published: 2005-01-13
Total Pages: 532
ISBN-13: 1420035215
DOWNLOAD EBOOKThe origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundame
Author: Isaac Woungang
Publisher: World Scientific
Published: 2010
Total Pages: 725
ISBN-13: 9812837175
DOWNLOAD EBOOKPt. 1. Applications of coding theory to computational complexity. ch. 1. Linear complexity and related complexity measures / Arne Winterhof. ch. 2. Lattice and construction of high coding gain lattices from codes / Mohammd-Reza Sadeghi. ch. 3. Distributed space-time codes with low ML decoding complexity / G. Susinder Rajan and B. Sundar Rajan -- pt. 2. Methods of algebraic combinatorics in coding theory/codes construction and existence. ch. 4. Coding theory and algebraic combinatorics / Michael Huber. ch. 5. Block codes from matrix and group rings / Paul Hurley and Ted Hurley. ch. 6. LDPC and convolutional codes from matrix and group rings / Paul Hurley and Ted Hurley. ch. 7. Search for good linear codes in the class of quasi-cyclic and related codes / Nuh Aydin and Tsvetan Asamov -- pt. 3. Source coding/channel capacity/network coding. ch. 8. Applications of universal source coding to statistical analysis of time series / Boris Ryabko. ch. 9. Introduction to network coding for acyclic and cyclic networks / Ángela I. Barbero and Øyvind Ytrehus. ch. 10. Distributed joint source-channel coding on a multiple access channel / Vinod Sharma and R. Rajesh -- pt. 4. Other selected topics in information and coding theory. ch. 11. Low-density parity-check codes and the related performance analysis methods / Xudong Ma. ch. 12. Variable length codes and finite automata / Marie-Pierre Béal [und weitere]. ch. 13. Decoding and finding the minimum distance with Gröbner Bases : history and new insights / Stanislav Bulygin and Ruud Pellikaan. ch. 14. Cooperative diversity systems for wireless communication / Murat Uysal and Muhammad Mehboob Fareed. ch. 15. Public key cryptography and coding theory / Pascal Véron
Author: Robert Fitzgerald Morse
Publisher: American Mathematical Soc.
Published: 2014-02-13
Total Pages: 202
ISBN-13: 0821894358
DOWNLOAD EBOOKThis volume contains the proceedings of the International Conference on Group Theory, Combinatorics and Computing held from October 3-8, 2012, in Boca Raton, Florida. The papers cover a number of areas in group theory and combinatorics. Topics include finite simple groups, groups acting on structured sets, varieties of algebras, classification of groups generated by 3-state automata over a 2-letter alphabet, new methods for construction of codes and designs, groups with constraints on the derived subgroups of its subgroups, graphs related to conjugacy classes in groups, and lexicographical configurations. Application of computer algebra programs is incorporated in several of the papers. This volume includes expository articles on finite coverings of loops, semigroups and groups, and on the application of algebraic structures in the theory of communications. This volume is a valuable resource for researchers and graduate students working in group theory and combinatorics. The articles provide excellent examples of the interplay between the two areas.
Author: Thomas Beth
Publisher: Cambridge University Press
Published: 1999-11-18
Total Pages: 524
ISBN-13: 9780521772310
DOWNLOAD EBOOKThis is the second edition of the standard text on design theory. Exercises are included throughout, and the book concludes with an extensive and updated bibliography of well over 1800 items.
Author: Dean Crnković
Publisher: IOS Press
Published: 2011
Total Pages: 460
ISBN-13: 1607506629
DOWNLOAD EBOOK"Published in cooperation with NATO Emerging Security Challenges Division"--T.p.
Author: Kathleen Quinn
Publisher: CRC Press
Published: 1999-01-29
Total Pages: 164
ISBN-13: 9780849306594
DOWNLOAD EBOOKThe fruit of a conference that gathered seven very active researchers in the field, Combinatorial Design and their Applications presents a wide but representative range of topics on the non-geometrical aspects of design theory. By concentrating on a few important areas, the authors succeed in providing greater detail in these areas in a more complete and accessible form. Through their contributions to this collection, they help fill a gap in the available combinatorics literature. The papers included in this volume cover recent developments in areas of current interest, such as difference sets, cryptography, and optimal linear codes. Researchers in combinatorics and other areas of pure mathematics, along with researchers in statistics and computer design will find in-depth, up-to-date discussions of design theory and the application of the theory to statistical design, codes, and cryptography.