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Pure Mathematics 2020
由GRS码构造新的量子MDS码
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Abstract:
量子MDS码的构造如今变得越来越重要。本文我们对q2-1作素数分解并讨论了q的奇偶性,在有限域Fq2上构造了4类新的量子MDS码。这些量子MDS码参数更灵活,最小距离大。此外,我们通过L1-forms和L2-forms可以找到那些极小距离大于q/2+1的那些量子MDS码。
It becomes more important to construct quantum maximum-distance-separable (MDS) codes by means of the self-dual Generalized Reed-Solomon (GRS) codes. In this paper, we construct four classes of quantum MDS codes over a finite field Fq2 through the prime decomposition of q2-1 and the discussion of the parity of q. These quantum MDS codes have more flexible parameters with large minimum distance. Further, those quantum codes of the minimum distances larger than q/2+1 can be found by L1-forms and L2-forms.
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