Advances in coding theory and crytography / editors T. Shaska ... [et al.].

Format:

Book

Conference/Event

Contributor:

Conference in Coding Theory and Crytology (2007 : Vlore, Albania)

Applications of Computer Algebra Conference (2007 : Oakland University)

Shaska, Tony, 1967-

Conference Name:

Vlora Conference in Coding Theory and Cryptography (2007 : Vlorë, Albania)

Applications of Computer Algebra Conference (2007 : Oakland University)

Series:

Series on coding theory and cryptology ; 3.

Series on coding theory and cryptology ; v. 3

Language:

English

Subjects (All):

Coding theory--Congresses.

Coding theory.

Cryptography--Congresses.

Cryptography.

Physical Description:

1 online resource (268 p.)

Edition:

1st ed.

Place of Publication:

New Jersey : World Scientific, c2007.

Language Note:

English

Summary:

In the new era of technology and advanced communications, coding theory and cryptography play a particularly significant role with a huge amount of research being done in both areas. This book presents some of that research, authored by prominent experts in the field.The book contains articles from a variety of topics most of which are from coding theory. Such topics include codes over order domains, Groebner representation of linear codes, Griesmer codes, optical orthogonal codes, lattices and theta functions related to codes, Goppa codes and Tschirnhausen modules, s-extremal codes, automorph

Contents:

Preface; List of authors; CONTENTS; The key equation for codes from order domains J. B. Little; 1. Introduction; 2. Codes from Order Domains; 3. Preliminaries on Inverse Systems; 4. The Key Equation and its Relation to the BMS Algorithm; Acknowledgements; References; A Grobner representation for linear codes M. Borges-Quintana, M. A. Borges-Trenard and E. Mart nez-Moro; 1. Introduction; 2. M ̈oller's algorithm; 3. Gr ̈obner representation of a linear code; 4. Reduced and border bases; 4.1. Binary codes; 5. Applications; 5.1. Gradient decoding; 5.2. Permutation equivalent codes

5.3. Gr ̈obner codewords for binary codesAcknowledgments; References; Arcs, minihypers, and the classification of three-dimensional Griesmer codes H. N. Ward; 1. Introduction; 2. Codes and the Griesmer bound; 3. Codes and multisets; 3.1. Arcs; 3.2. Combinations; 4. Minihypers; 4.1. The Hamada bound; 4.2. Achievement of the Griesmer bound; 5. Divisibility; 6. Three-dimensional Griesmer codes; 6.1. Orphans; 6.2. Divisibility; 6.3. The [92, 3, 80]8 codes; 6.4. Duality; Acknowledgment; References; Optical orthogonal codes from Singer groups T. L. Alderson and K. E. Mellinger; 1. Introduction

2. Preliminaries 3. A construction from arcs in d-flats; 4. A construction from arcs of higher degree; 5. Affine constructions; 6. Conclusion; Acknowledgments; References; Codes over Fp 2 and Fp x Fp, lattices, and theta functions T. Shaska and C. Shor; 1. Introduction; 2. Preliminaries; 2.1. Theta functions over Fp; 3. Theta functions of codes over R; 3.1. A MacWilliams identity; 3.2. A generalization of the symmetric weight enumerator polynomial; 4. The injectivity of construction A; 4.1. The case p = 2; 4.2. The case p > 2; Acknowledgment; References

Goppa codes and Tschirnhausen modules D. Coles and E. PreviatoIntroduction; 1. Goppa Codes and rank-2 Vector Bundles; 2. The Klein Curve as Cover; 3. The Tschirnhausen Module of the Cover; 4. Goppa Codes and Adeles; 4.1. Adeles and pseudo-differentials; 4.2. Goppa codes and adeles; Acknowledgements; References; Remarks on s-extremal codes J.-L. Kim; 1. Introduction; 2. s-Extremal Additive F4 Codes; 3. s-Extremal Binary Codes; 4. Conclusion; Acknowledgments; References; Automorphism groups of generalized Reed-Solomon codes D. Joyner, A. Ksir and W. Traves; 1. Introduction

2. AG codes and GRS codes 3. Automorphisms; 4. Examples; 5. Structure of the representations; References; About the code equivalence I. G. Bouyukliev; 1. Introduction; 2. Codes and binary matrices; 2.1. Equivalence of linear codes; 2.2. Isomorphism of binary matrices; 2.3. The connection between equivalence of linear codes and isomorphism of binary matrices; 3. Orbits, partitions, invariants; 3.1. Orbits; 3.2. Partitions, ordered partitions; 3.3. Definition of invariants; 3.4. Properties of partitions induced by invariants; 3.5. Invariants of columns and rows; 4. Main algorithm

4.1. Additional invariants

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611911898

9781281911896

1281911895

9789812772022

9812772022

OCLC:

828180122