Asymptotic Combinatorial Coding Theory
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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arbitrary set asymptotic upper bound average probability Bassalygo binary code binary symbols Blinovsky channel Chebyshev's inequality code Ank codevectors codewords columns combinatorial coding theory complexity coordinates coset decoding algorithm decoding error defined Denote EL(R elements equal probability exceed exists the code finite following equality following inequality following relations function Hamming bound Hamming code Hamming distance Hamming space Hamming weight Hausdorff dimension Hence inequality is valid Information Transmission inner code integer interval l)-covering packing last inequality Lemma length linear code linear independent list decoding lower bound matrix G minimum distance decoding obtain the estimate offer to prove orthonormal representation PA(L parameters Pinsker Pn(p prefix code probability of error Problems of Information Problemy Peredachi Informatsii rA(L random variables Reed-Solomon code relation is valid right hand side rows satisfy the relation space F sphere packing subsets Substituting Suppose TA(L Theorem upper bound Varshamov-Gilbert bound vertexes Zyablov