On enumeration of the perfect binary codes of length 15
نویسندگان
چکیده
منابع مشابه
Properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16
Properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16 Abstract. Some properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16 are presented for reference purposes. The attached files contain some tab-delimited properties of perfect binary codes of length 15 and extended per...
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We enumerate the extended perfect I-error correcting binary codes of length 16 which can be constructed by the concatenation or doubling construction. In the process, we establish some properties of these codes and consider algorithms that effectively establish the nonequivalence of these codes.
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Properties of nonlinear perfect binary codes are investigated and several new constructions of perfect codes are derived from these properties. An upper bound on the cardinality of the intersection of two perfect codes of length n is presented, and perfect codes whose intersection attains the upper bound are constructed for all n. As an immediate consequence of the proof of the upper bound we o...
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An (n, k) binary self-orthogonal code is an (n, k) binary linear code C that is contained in its orthogonal complement C⊥. A self-orthogonal code C is self-dual if C = C⊥. Two codes, C1 and C2, are equivalent if and only if there exists a coordinate permutation of C1 that takes C1 into C2. The automorphism group of a code C is the set of all coordinate permutations of C that takes C into itself...
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A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 is presented. There are 5 983 such inequivalent perfect codes and 2 165 extended perfect codes. Efficient generation of these codes relies on the recent classification of Steiner quadruple systems of order 16. Utilizing a result of Blackmore, the optimal binary one-er...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2004
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(02)00303-7