A course in algebraic error-correcting codes. (2020)

• Record Type: Book
• Further Information: Note: Simeon Ball.
• Other Names: Ball, Simeon (Simeon Michael)
• Contents: Intro -- Preface -- Table of Parameters for Codes in the Text -- Contents -- 1 Shannon's Theorem -- 1.1 Entropy -- 1.2 Information Channels -- 1.3 System Entropies and Mutual Information -- 1.4 Decoding and Transmission Rate -- 1.5 Shannon's Theorem -- 1.6 Comments -- 1.7 Exercises -- 2 Finite Fields -- 2.1 Definitions and Construction -- 2.2 Properties of Finite Fields -- 2.3 Factorisation of Cyclotomic Polynomials -- 2.4 Affine and Projective Spaces over Finite Fields -- 2.5 Comments -- 2.6 Exercises -- 3 Block Codes -- 3.1 Minimum Distance -- 3.2 Bounds on Block Codes 3.3 Asymptotically Good Codes -- 3.4 Comments -- 3.5 Exercises -- 4 Linear Codes -- 4.1 Preliminaries -- 4.2 Syndrome Decoding -- 4.3 Dual Code and the MacWilliams Identities -- 4.4 Linear Codes and Sets of Points in Projective Spaces -- 4.5 Griesmer Bound -- 4.6 Constructing Designs from Linear Codes -- 4.7 Comments -- 4.8 Exercises -- 5 Cyclic Codes -- 5.1 Basic Properties -- 5.2 Quadratic Residue Codes -- 5.3 BCH Codes -- 5.4 Comments -- 5.5 Exercises -- 6 Maximum Distance Separable Codes -- 6.1 Singleton Bound -- 6.2 Reed-Solomon Code -- 6.3 Linear MDS Codes -- 6.4 MDS Conjecture 6.5 Comments -- 6.6 Exercises -- 7 Alternant and Algebraic Geometric Codes -- 7.1 Subfield Subcodes -- 7.2 Generalised Reed-Solomon Codes -- 7.3 Alternant Codes Meeting the Gilbert-Varshamov Bound -- 7.4 Algebraic Geometric Codes -- 7.5 Algebraic Geometric Codes Surpassing the Gilbert-Varshamov Bound -- 7.6 Comments -- 7.7 Exercises -- 8 Low Density Parity Check Codes -- 8.1 Bipartite Graphs with the Expander Property -- 8.2 Low Density Parity Check Codes -- 8.3 Decoding LDPC Codes -- 8.4 Comments -- 8.5 Exercises -- 9 Reed-Muller and Kerdock Codes -- 9.1 Binary Reed-Muller Codes 9.2 Decoding Reed-Muller Codes -- 9.3 Kerdock Codes -- 9.4 Non-binary Reed-Muller Codes -- 9.5 Comments -- 9.6 Exercises -- 10 p-Adic Codes -- 10.1 p-Adic Numbers -- 10.2 Polynomials over the p-Adic Numbers -- 10.3 p-Adic Codes -- 10.4 Codes over Z/phZ -- 10.5 Codes over Z/4Z -- 10.6 Comments -- 10.7 Exercises -- Hints and Answers to Selected Exercises -- Bibliography -- Index
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (185 p.)
• Subjects: 005.7/17; Error-correcting codes (Information theory); Error-correcting codes (Information theory); Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030411534; 3030411532
• Related ISBNs: 9783030411527; 3030411524
• Notes: Note: Includes bibliographical references and index.
• 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.