Asymptotic Combinatorial Coding Theory
Springer Science & Business Media, Aug 31, 1997 - Technology & Engineering - 93 pages
Asymptotic Combinatorial Coding Theory is devoted to the investigation of the combinatorial properties of transmission systems using discrete signals. The book presents results of interest to specialists in combinatorics seeking to apply combinatorial methods to problems of combinatorial coding theory.
Asymptotic Combinatorial Coding Theory serves as an excellent reference for resarchers in discrete mathematics, combinatorics, and combinatorial coding theory, and may be used as a text for advanced courses on the subject.
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algorithm arbitrary asymptotic average radius ball belong binary Blinovsky called cardinality channel Chapter choose chosen codevectors codewords coding theory columns combinatorial complexity consequently consider construct contains coordinates corresponding covering decoding defects defined definition Denote density dimension easy elements ensemble equal error estimate event exceed exists expression finite fixed following inequality following relations function given graph greater Hamming Hence independent inequality integer interval introduce l)-covering Lemma length less linear code matrix maximal method minimum distance necessary Note obtain obtain the estimate output packing parameters points positions prefix probability Problem procedure proof prove random relation is valid result right hand side rows Russian satisfy the relation sequence Statement step subsets Substituting Suppose symbols Theorem UL+I upper bound valid variables vectors vertexes zero