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International Conference on Future Networks

Quantum Codes of Minimum Distance Three Constructed from Binary Codes of Odd Length

Ruihu Li, Gang Chen

Published Jan 1, 2010• 1 citation
Publisher

Abstract

We give elementary recursive constructions of a pair of nested binary self-orthogonal codes with dual distance two and three for all odd n ¿ 11. Consequently, good quantum codes of minimum distance three for such length n are obtained via Steane's construction. Such quantum codes were explicitly constructed before only for a sparse set of lengths.

DOI
10.1109/icfn.2010.20

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We give elementary recursive constructions of a pair of nested binary self-orthogonal codes with dual distance two and three for all odd n ¿ 11. Consequently, good quantum codes of minimum distance three for such length n are obtained via Steane's construction. Such quantum codes were explicitly constructed before only for a sparse set of lengths.
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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.
In this paper, a special subclass of binary generalized quasi-cyclic self-orthogonal codes and quantum codes constructed by Steane construction are discussed.Firstly, eight 16-dimensional even length generalized quasi-cyclic self-orthogonal codes with dual distance five are built based on circulant or partial circulant matrices.Secondly, pairs of nested self-orthogonal codes with dual distance five and three are designed by applying an algorithm for searching subcodes of a given code.Thirdly, revised pairs of codes with dual distance six and four are constructed by extending previous pairs of codes, and then eight quantum codes with distance six are obtained by Steane construction.These eight quantum codes are new binary construction by Steane construction and are best known ones.