%0 Journal Article
%T 由GRS码构造新的量子MDS码<br>New Quantum MDS Codes from GRS Codes
%A 陈硕
%A 唐西林
%J Pure Mathematics
%P 876-888
%@ 2160-7605
%D 2020
%I Hans Publishing
%R 10.12677/PM.2020.109102
%X <p align=\"justify\">
	量子MDS码的构造如今变得越来越重要。本文我们对q<sup>2</sup>-1作素数分解并讨论了q的奇偶性，在有限域F<sub>q<sup>2</sup></sub>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L<sub>1</sub>-forms和L<sub>2</sub>-forms可以找到那些极小距离大于q/2+1的那些量子MDS码。<br />
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 F<sub>q<sup>2</sup></sub> through the prime decomposition of q<sup>2</sup>-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 L<sub>1</sub>-forms and L<sub>2</sub>-forms.
</p>
%K 量子码，厄米特自正交，GRS码<br>Quantum MDS Code
%K Hermitian Self-Orthogonal
%K GRS Codes
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=37808