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International Conference on Machine Learning and Cybernetics

Non-binary quantum codes constructed from classical BCH codes

You Gao, Ya-Yuan Tao

Published Jul 1, 2010• 1 citation
Publisher

Abstract

Let q be a power of an odd prime number p. We use finite fields to character q-ary BCH codes, then use puncturing and gluing methods to construct self-orthogonal BCH codes. Finally we obtain families of q-ary quantum codes by using the self-orthogonal BCH codes constructed.
DOI
10.1109/icmlc.2010.5580593

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Let R= Fq+uFq+vFq+uvFq be a commutative ring with u2=u, v2=v, uv=vu, where q is a power of an odd prime. Ashraf and Mohammad constructed some new quantum codes from cyclic codes. Under this background, another Gray map from R to Fq4 is given. This map can be naturally extended to Rn. The problem on the ring turns to the field by this isomorphic map now. Therefore, This mapping is obviously a weight-preserving and distance-preserving map. The results show that the codes after mapping are self-orthogonal codes over Fq if they are self-orthogonal codes over R. Some computational examples show that some better non-binary quantum codes can be obtained under this Gray map. We discuss the structure of linear codes. On this basis, the structure of the generating matrix of linear codes is obtained. The structure of their dual codes is also obtained. The CSS construction guarantees the existence of quantum codes. Finally, with the help of the CSS construction, we get some good quantum codes. By comparison, our quantum codes have better parameters.