Covering codes. (1997)

• Record Type: Book
• Further Information: Note: Gérard Cohen [and others].
• Other Names: Cohen, G (Gérard), 1951-
• Contents: Cover -- Contents -- Preface -- List of Symbols -- List of Tables -- Chapter 1. Introduction -- 1.1 Covering problems -- 1.2 Applications -- Chapter 2. Basic facts -- 2.1 Codes -- 2.2 The MacWilliams identities -- 2.3 Krawtchouk polynomials -- 2.4 Hamming spheres -- 2.5 Finite fields -- 2.6 Families of error-correcting codes -- 2.7 Designs, constant weight codes, graphs -- 2.8 Notes -- Chapter 3. Constructions -- 3.1 Puncturing and adding a parity check bit -- 3.2 Direct sum -- 3.3 Piecewise constant codes -- 3.4 Variations on the (u, u + v) construction -- 3.5 Matrix construction -- 3.6 Cascading -- 3.7 Optimal short nonbinary codes -- 3.8 Simulated annealing and local search -- 3.9 Notes -- Chapter 4. Normality -- 4.1 Amalgamated direct sum -- 4.2 Normality of binary linear codes -- 4.3 Abnormal binary nonlinear codes -- 4.4 Normality of binary nonlinear codes -- 4.5 Blockwise direct sum -- 4.6 Notes -- Chapter 5. Linear constructions -- 5.1 Basic facts about linear covering codes -- 5.2 The case R = 1; examples of small codes -- 5.3 Saving more than one coordinate -- 5.4 Davydov's basic construction -- 5.5 Notes -- Chapter 6. Lower bounds -- 6.1 Bounds for the cardinality of the union of K spheres -- 6.2 Balanced codes -- 6.3 Excess bounds for codes with covering radius one -- 6.4 Excess bounds for codes with arbitrary covering radius -- 6.5 The method of linear inequalities -- 6.6 Table on K (n, R) -- 6.7 Lower bounds for nonbinary codes -- 6.8 Notes -- Chapter 7. Lower bounds for linear codes -- 7.1 Excess bounds for linear codes -- 7.2 Linear codes with covering radius two and three -- 7.3 Tables for linear codes -- 7.4 Notes -- Chapter 8. Upper bounds -- 8.1 Codes with given size and distance -- 8.2 Covering radii of subcodes -- 8.3 Covering radius and dual distance -- 8.4 Notes -- Chapter 9. Reed-Muller codes -- 9.1 Definitions and properties -- 9.2 First order Reed-Muller codes -- 9.3 Reed-Muller codes of order 2 and m -- 3 -- 9.4 Covering radius of Reed-Muller codes of arbitrary order -- 9.5 Notes -- Chapter 10. Algebraic codes -- 10.1 BCH codes: definitions and properties -- 10.2 2-and 3-error-correcting BCH codes -- 10.3 Long BCH codes -- 10.4 Normality of BCH codes -- 10.5 Other algebraic codes -- 10.6 Notes -- Chapter 11. Perfect codes -- 11.1 Perfect linear codes over IFq -- 11.2 A nonexistence result -- 11.3 Enumeration of perfect binary codes -- 11.4 Enumeration of perfect codes over Fq -- 11.5 Mixed codes -- 11.6 Generalizations of perfect codes -- 11.7 Notes -- Chapter 12. Asymptotic bounds -- 12.1 Covering radius of unrestricted codes -- 12.2 Greedy algorithm and good coverings -- 12.3 Covering radius of hnear codes -- 12.4 Density of coverings -- 12.5 Coverings of small size -- 12.6 Bounds on the minimum distance -- T$
• Publisher Details: Place of publication not identified : North Holland
• Publication Date: 1997
• Extent: 1 online resource (541 pages)
• Subjects: 003/.54; Combinatorial packing and covering; enveloppe convexe; code; géométrie algorithmique; recouvrement; espace euclidien; Combinatorial packing and covering
• Languages: English
• ISBNs: 9780080530079; 0080530079
• 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.