منابع مشابه
On Z2k-Dual Binary Codes
A new generalization of the Gray map is introduced. The new generalization Φ : Z 2 → Z k−1 n 2 is connected with the known generalized Gray map φ in the following way: if we take two dual linear Z2k -codes and construct binary codes from them using the generalizations φ and Φ of the Gray map, then the weight enumerators of the binary codes obtained will satisfy the MacWilliams identity. The cla...
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There is a large gap between Zhang’s theoretical bound for the length n of a binary extremal self-dual doublyeven code and what we can construct. The largest n is 136. In order to find examples for larger n a non-trivial automorphism group might be helpful. In the list of known examples extended quadratic residue codes and quadratic double circulant codes have large automorphism groups. But in ...
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Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual [n, k] codes with the largest minimum weight among all binary linear complementary dual [n, k] codes. We characterize binary linear complementary dual codes with the largest minimum weight for small dimensions. A complete ...
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The goal of this thesis is to explore the interplay between binary self-dual codes and the \'etale cohomology of arithmetic schemes. Three constructions of binary self-dual codes with arithmetic origins are proposed and compared: Construction $\Q$, Construction G and the Equivariant Construction. In this thesis, we prove that up to equivalence, all binary self-dual codes of length at least $4$ ...
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In this paper, we study binary optimal odd formally self-dual codes. All optimal odd formally self-dual codes are classified for length up to 16. The highest minimum weight of any odd formally self-dual codes of length up to 24 is determined. We also show that there is a unique linear code for parameters [16, 8, 5] and [22, 11, 7], up to equivalence.
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2007
ISSN: 0018-9448
DOI: 10.1109/tit.2007.892787