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Computer Engineering and Applications Journal

Binary minimum self-orthogonal codes of dual distance five and their subcodes

Luobin Guo

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The equivalence of maximal self-orthogonal codes obtained from binary self-dual codes by truncating are discussed.Many non-equivalent maximal self-orthogonal codes of length 21≤n≤29 and dual distance five are constructed by truncating self-dual codes of dual distance six.Subcodes of these maximal self-orthogonal codes are studied by using of a random search algorithm,and the subcodes of dual distance 3 and 5 of these maximal self-orthogonal codes are constructed.The code chains of these self-orthogonal subcodes and the S-chains obtained from the dual of these self-orthogonal subcodes are also determined.According to Steane’s construction,some very good quantum codes of distance five are constructed by the obtained S-chains.

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Journal of Air Force Engineering University•Jan 1, 2008•0 citations
The equivalence of maximal self-orthogonal codes obtained from binary self-dual codes by truncating are discussed.Many non-equivalent maximal self-orthogonal codes of length 21≤n≤29 and dual distance five are constructed by truncating self-dual codes of dual distance six.Subcodes of these maximal self-orthogonal codes are studied by using of a random search algorithm,and the subcodes of dual distance 3 and 5 of these maximal self-orthogonal codes are constructed.The code chains of these self-orthogonal subcodes and the S-chains obtained from the dual of these self-orthogonal subcodes are also determined.According to Steane’s construction,some very good quantum codes of distance five are constructed by the obtained S-chains.
The subcodes of binary self-dual codes whose length n between 22 and 30 and minimum distance six are studied by using of a random search algorithm,and the subcodes of dual distance 3,4,5 and 6 of these self-dual codes are constructed.The code chains of these self-orthogonal subcodes and the S-chains obtained from the dual of these self-orthogonal subcodes are also determined.According to Steane’s construction,some very good quantum codes of distance five and six are constructed by the obtained S-chains,and some of these quantum codes have improved parameters than previously known codes.
Subcodes of some known maximal self-orthogonal codes and optimal self-dual codes of length n between 9 and 22 over F5 are studied. Using a random search algorithm, we construct subcodes with given dual distance 2, 3, 4, 5 and 6 from these known codes, and discuss code chains formed by obtained subcodes and their dual codes. Based on these obtained code chains, we construct many quantum codes of distance 3, 4, 5, 6 and 8 by using of Steane's construction, some of these quantum codes are present known best codes.
Quantum error-correcting codes protect quantum information against undesirable noise in quantum computation and quantum communication.It is one of important problems that constructing very good quantum codes.There are two methods that use binary codes to construct quantum codes,one is CSS construction,another is Steane construction.These two methods are all based on the construction of binary self-orthogonal codes.Combinational construction of binary self-orthogonal codes is investigated in this paper.From known codes chains of binary self-orthogonal codes and their dual codes chains with given dual distance,new binary self-orthogonal codes of dual distance three,four,five and six are constructed.Based on these results,for each satisfying,S-chains with parameters and are constructed.According to Steane's construction,many very good quantum codes of distance five and six are constructed by the obtained S-chains,some of these quantum codes are new and some of these quantum codes have improved parameters than previously known codes.
The method of constructing quantum error-correcting code by the quaternary self-orthogonal sub-code chains and L-chains are investigated in this paper.Random searching method is used to find quaternary self-orthogonal codes and these self-orthogonal codes could form some self-orthogonal code chains.By using combinatorial method,quantum error-correcting codes are constructed in light of L-chains which are constructed by dual of these self-orthogonal codes.The code chains of these self-orthogonal sub-codes and the L-chains which are obtained from the dual of these self-orthogonal sub-codes of length n between 20 and 36 and n=40,45,50,55,60 and dual distance five and six are determined.Some quantum codes of distance five and six are constructed by the obtained L-chains,some quantum error-correcting codes are new.