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Computer Engineering and Applications Journal

Optimal quaternary self-orthogonal code chains of short code length

Yiqun Li

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The optimal quaternary self-orthogonal code reaching the bound of Griesmer is studied.By the methods of combination and the random search algorithm,the self-orthogonal code chains of short code length n(10≤n≤19) are constructed in the filed of GF(4).One result of the optimal self-orthogonal code chains with code length n(10≤n≤19) is given in this paper,and the parameters of codes in which meet the Griesmer bound.The results are important references to farther researching the construction of the self-orthogonal code chain and quantum code.

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The optimal quaternary self-orthogonal code reaching the bound of Griesmer is studied.By the methods of combination and the random search algorithm,the self-orthogonal code chains of short code length n(10≤n≤19) are constructed in the filed of GF(4).One result of the optimal self-orthogonal code chains with code length n(10≤n≤19) is given in this paper,and the parameters of codes in which meet the Griesmer bound.The results are important references to farther researching the construction of the self-orthogonal code chain and quantum code.
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By using construction arithmetic,the subcodes of quaternary self-dual codes with code length 10≤n≤20 are studied and seve-ral self-orthogonal codes' matrixes with dual distance 3,4,5 and 6 are constructed.The series of the self-dual and self-orthogonal chains are constructed by these matrixes and the subcodes' L-chains with maximal dual distance are deduced.In the end,some quantum error correct codes are constructed by using these quaternary subcodes' L-chains and the construction theory of additive quantum error correct code.Some quantum error correct codes with good parameters are better than previously known.
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For a given quaternary self-orthogonal (SO) code, using information of weights of codewords in the dual of the binary code generated by the supports of this SO code, one can construct new quaternary SO code by shortening method. Two methods of determining weights of codewords in the dual of the binary support code of a given large length SO code are presented. Using these methods, we construct many SO codes from a quantum 286-cap in PG(6, 4), and deduce existence of many quantum caps in PG(6, 4) and good quantum codes of distance 4.