Introduction to Coding Theory. (2004)

• Record Type: Book
• Further Information: Note: Jurgen Bierbrauer.
• Authors: Bierbrauer, Jurgen
• Contents: Cover; Half Title; Title Page; Copyright Page; Preface; About the author; Dedication; Table of Contents; I: An elementary introduction to coding; 1: The concept of coding; 1.1 Bitstrings and binary operations; 1.2 The Hamming distance; 1.3 Binary codes; 1.4 Error-correcting codes in general; 1.5 The binary symmetric channel; 1.6 The sphere-packing bound; 2: Binary linear codes; 2.1 The concept of binary linear codes; 2.2 Block coding; 2.3 The effect of coding; 2.4 Duality; 2.5 Binary Hamming and Simplex codes; 2.6 Principle of duality; 3: General linear codes; 3.1 Prime fields 3.2 Finite fields3.3 Linear codes over finite fields; 3.4 Duality and orthogonal arrays; 3.5 Weight distribution; 3.6 The game of SET; 3.7 Syndrome decoding; 4: Singleton bound and Reed-Solomon codes; 5: Recursive constructions I; 5.1 Shortening and puncturing; 5.2 Concatenation; 6: Universal hashing; 7: Designs and the binary Golay code; 8: Shannon entropy; 9: Asymptotic results; 10: 3-dimensional codes, projective planes; 11: Summary and outlook; II: Theory and applications of codes; 12: Subfield codes and trace codes; 12.1 The trace; 12.2 Trace codes and subfield codes 12.3 Galois closed codes12.4 Automorphism groups; 13: Cyclic codes; 13.1 Some primitive cyclic codes of length 15; 13.2 Theory of cyclic codes; 13.3 Decoding BCH-codes; 13.4 Constacyclic codes; 13.5 Remarks; 14: Recursive constructions, covering radius; 14.1 Construction X; 14.2 Covering radius; 15: OA in statistics and computer science; 15.1 OA and independent random variables; 15.2 Linear shift register sequences; 15.3 Cryptography; 15.4 Two-point based sampling; 15.5 Resilient functions; 15.6 Derandomization of algorithms; 15.7 Authentication and universal hashing 16: The geometric description of codes16.1 Linear codes as sets of points; 16.2 Quadratic forms, bilinear forms and caps; 16.3 Caps: constructions and bounds; 17: Additive codes; 17.1 Basic constructions and applications; 17.2 Additive cyclic codes; 17.3 Quantumcodes; 18: The last chapter; 18.1 The linear-programming bound; 18.2 Algebraic-geometric codes; 18.3 List decoding; 18.4 Expander codes; 18.5 tms-nets; 18.6 Sphere packings; 18.7 Designs; 18.8 Nonlinear codes; References; Index
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2004
• Extent: 1 online resource
• Subjects: 003/.54; Combinatorial analysis; Computer engineering; Cryptography; Combinatorial analysis; Computer engineering; Cryptography; Electronic books
• Languages: English
• ISBNs: 9781482296372; 1482296373
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.