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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.
The classification of binary [n,k,d] codes with d ges s2k-1 and without zero coordinates is reduced to the classification of binary [(2k-1)c (k,s,t)+t,k,d] code for n =(2k-1)s+t, s ges 1 and 1 les t les 2k-2, where c(k,s,t) les min{s, t} is a function of k, s, and t. Binary [15s +t, 4] optimal self-orthogonal codes are characterized by systems of linear equations. Based on these two results, the complete...
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...
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