05604nam 2200697Ia 450 991045093380332120210706194058.01-281-91189-59786611911898981-277-202-2(CKB)1000000000410510(EBL)1193247(SSID)ssj0000288091(PQKBManifestationID)12106010(PQKBTitleCode)TC0000288091(PQKBWorkID)10372360(PQKB)11295799(MiAaPQ)EBC1193247(WSP)00006464(Au-PeEL)EBL1193247(CaPaEBR)ebr10698865(CaONFJC)MIL191189(OCoLC)828180122(EXLCZ)99100000000041051020070427d2007 uy 0engur|n|---|||||txtccrAdvances in coding theory and crytography[electronic resource] /editors T. Shaska ... [et al.]New Jersey World Scientificc20071 online resource (268 p.)Series on coding theory and cryptology ;v. 3Description based upon print version of record.981-270-701-8 Includes bibliographical references.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 codes5.3. 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. Introduction2. 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; ReferencesGoppa 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. Introduction2. 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 algorithm4.1. Additional invariantsIn 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, automorphSeries on coding theory and cryptology ;3.Coding theoryCongressesCryptographyCongressesElectronic books.Coding theoryCryptography003/.54Shaska Tony1967-933047Conference in Coding Theory and Crytology(2007 :Vlore, Albania)Applications of Computer Algebra Conference(2007 :Oakland University)MiAaPQMiAaPQMiAaPQBOOK9910450933803321Advances in coding theory and crytography2100088UNINA