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Quantum Information Processing

Self-orthogonal codes with dual distance three and quantum codes with distance three over $$\mathbb F _5$$ F 5

Fangchi Liang

Published Aug 9, 2013• 4 citations
Publisher
DOI
10.1007/s11128-013-0620-y

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Self-orthogonal codes with dual distance three and quantum codes with distance three over F5\mathbb F _5F5​ F 5
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.
New quantum codes from self-dual codes over F4\mathbb {F}_4F4​
A heuristic algorithm is designed to searching for good higher dimensional self-orthogonal codes over GF(A) from low dimensional self-orthogonal codes. Many self-orthogonal codes of length 20 les n les 36 and dual distance 5 or 6 are obtained, and several have improved dual distance. Consequently, using these self-orthogonal codes and their dual codes, some linear quantum codes of minimum distance five or six for such length n are obtained, and three of these codes [[24, 8, 5]], [[25, 9, 5]], [[27, 7, 6]] are record-breaking. Quaternary code, self-orthogonal code, linear quantum error-correcting code.