1. Covering codes [1997]
 New York : Elsevier Science, 1997.
 Description
 Book — xix, 542 p. ; 23 cm.
 Summary

 Introduction. Covering problems. Applications. Basic Facts. Codes. The MacWilliams identities. Krawtchouk polynomials. Hamming spheres. Finite fields. Families of errorcorrecting codes. Designs, constant weight codes, graphs. Constructions. Puncturing and adding a parity check bit. Direct sum. Piecewise constant codes. Variations on the (u, u + v) construction. Matrix construction. Cascading. Optimal short nonbinary codes. Simulated annealing and local search. Normality. Amalgamated direct sum. Normality of binary linear codes. Abnormal binary nonlinear codes. Normality of binary nonlinear codes. Blockwise direct sum. Linear Constructions. Basic facts about linear covering codes. The case R=1
 examples of small codes. Saving more than one coordinate. Davydov's basic construction. Lower Bounds. Bounds for the cardinality of the union of K spheres. Balanced codes. Excess bounds for codes with covering radius one. Excess bounds for codes with arbitrary covering radius. The method of linear inequalities. Table on K(n, R). Lower bounds for nonbinary codes. Lower Bounds for Linear Codes. Excess bounds for linear codes. Linear codes with covering radius two and three. Tables for linear codes. Upper Bounds. Codes with given size and distance. Covering radii of subcodes. Covering radius and dual distance. ReedMuller Codes. Definitions and properties. First order ReedMuller codes. ReedMuller codes of order 2 and m3. Covering radius of ReedMuller codes of arbitrary order. Algebraic Codes. BCH codes: definitions and properties. 2 and 3errorcorrecting BCH codes. Long BCH codes. Normality of BCH codes. Other algebraic codes. Perfect Codes. Perfect linear codes over IFq. A nonexistence result. Enumeration of perfect binary codes. Enumeration of perfect codes over IFq. Mixed codes. Generalizations of perfect codes. Asymptotic Bounds. Covering radius of unrestricted codes. Greedy algorithm and good coverings. Covering radius of linear codes. Density of coverings. Coverings of small size. Bounds on the minimum distance. Covering radius as a function of dual distance. Packing radius vs covering radius. Weighted Coverings. Basic notions. Lloyd theorem for perfect weighted coverings. Perfect weighted coverings with radius one. Weighted coverings and nonexistence results. Multiple Coverings. Definitions. Perfect multiple coverings. Normality of multiple coverings. Constructions. Tables for multiple coverings. Multiple coverings of deep holes. Football Pools. Constructions for mixed binary/ternary codes. Tables for mixed binary/ternary codes. On the early history of the ternary Golay code. Tilings. Preliminaries. A sufficient condition. Small tiles. Periodicity of tilings. Recursive decomposition of tilings. Tilings and perfect binary codes. Nonexistence results. Writing on Constrained Memories. Worst case coverings and WOMs. The error case. A model for correcting single errors. Singleerrorcorrecting WOMcodes. Nonlinear WOMcodes. Subset Sums and Constrained Memories. Cayley graphs. Subset sums. Maximal sumfree sets. Constrained memories (W*Ms). Translationinvariant constraints. Domatic number and reluctant memories. Defective memories. The error case. Heterodox Coverings. Perfect coverings by Lspheres. Perfect coverings by spheres of two radii. Coverings by spheres all of different radii. Multicovering radius. Perfect coverings of a sphere and constant weight coverings. Complexity. Basic facts about the polynomial hierarchy. The complexity of computing the covering radius of a binary code. Derandomization. Bibliography. Index.
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Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

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QA166.7 .C68 1997  Unknown Request 