由GRS码构造新的量子MDS码
New Quantum MDS Codes from GRS Codes
DOI: 10.12677/PM.2020.109102, PDF,   
作者: 陈 硕, 唐西林：华南理工大学数学学院，广东 广州
关键词: 量子码；厄米特自正交；GRS码；Quantum MDS Code； Hermitian Self-Orthogonal； GRS Codes
摘要: 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。
Abstract: 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.
文章引用：陈硕, 唐西林. 由GRS码构造新的量子MDS码[J]. 理论数学, 2020, 10(9): 876-888. https://doi.org/10.12677/PM.2020.109102

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