LEADER 05604nam 2200697Ia 450 001 9910450933803321 005 20210706194058.0 010 $a1-281-91189-5 010 $a9786611911898 010 $a981-277-202-2 035 $a(CKB)1000000000410510 035 $a(EBL)1193247 035 $a(SSID)ssj0000288091 035 $a(PQKBManifestationID)12106010 035 $a(PQKBTitleCode)TC0000288091 035 $a(PQKBWorkID)10372360 035 $a(PQKB)11295799 035 $a(MiAaPQ)EBC1193247 035 $a(WSP)00006464 035 $a(Au-PeEL)EBL1193247 035 $a(CaPaEBR)ebr10698865 035 $a(CaONFJC)MIL191189 035 $a(OCoLC)828180122 035 $a(EXLCZ)991000000000410510 100 $a20070427d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aAdvances in coding theory and crytography$b[electronic resource] /$feditors T. Shaska ... [et al.] 210 $aNew Jersey $cWorld Scientific$dc2007 215 $a1 online resource (268 p.) 225 1 $aSeries on coding theory and cryptology ;$vv. 3 300 $aDescription based upon print version of record. 311 $a981-270-701-8 320 $aIncludes bibliographical references. 327 $aPreface; 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 327 $a5.3. 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 327 $a2. 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 327 $aGoppa 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 327 $a2. 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 327 $a4.1. Additional invariants 330 $aIn the new era of technology and advanced communications, coding theory and cryptography play a particularly significant role with a huge amount of research being done in both areas. This book presents some of that research, authored by prominent experts in the field.The book contains articles from a variety of topics most of which are from coding theory. Such topics include codes over order domains, Groebner representation of linear codes, Griesmer codes, optical orthogonal codes, lattices and theta functions related to codes, Goppa codes and Tschirnhausen modules, s-extremal codes, automorph 410 0$aSeries on coding theory and cryptology ;$v3. 606 $aCoding theory$vCongresses 606 $aCryptography$vCongresses 608 $aElectronic books. 615 0$aCoding theory 615 0$aCryptography 676 $a003/.54 701 $aShaska$b Tony$f1967-$0933047 712 02$aConference in Coding Theory and Crytology$f(2007 :$eVlore, Albania) 712 02$aApplications of Computer Algebra Conference$f(2007 :$eOakland University) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910450933803321 996 $aAdvances in coding theory and crytography$92100088 997 $aUNINA