关于有限域\(F\)上循环码的最优码与量子码构造及其应用
On Optimal and Quantum Code Construction from Cyclic Codes over F with Applications.
作者信息
Ali Shakir, Alali Amal S, Sharma Pushpendra, Wong Kok Bin, Öztas Elif Segah, Jeelani Mohammad
机构信息
Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.
出版信息
Entropy (Basel). 2023 Aug 2;25(8):1161. doi: 10.3390/e25081161.
The key objective of this paper is to study the cyclic codes over mixed alphabets on the structure of FqPQ, where P=Fq[v]⟨v3-α22v⟩ and Q=Fq[u,v]⟨u2-α12,v3-α22v⟩ are nonchain finite rings and αi is in Fq/{0} for i∈{1,2}, where q=pm with m≥1 is a positive integer and is an odd prime. Moreover, with the applications, we obtain better and new quantum error-correcting (QEC) codes. For another application over the ring , we obtain several optimal codes with the help of the Gray image of cyclic codes.
本文的关键目标是研究混合字母表上的循环码在(F_qPQ)的结构，其中(P = F_q[v]\langle v^3 - \alpha_2^2v\rangle)且(Q = F_q[u, v]\langle u^2 - \alpha_1^2, v^3 - \alpha_2^2v\rangle)是非链有限环，对于(i \in {1, 2})，(\alpha_i \in F_q / {0})，其中(q = p^m)，(m \geq 1)是正整数且(p)是奇素数。此外，通过这些应用，我们得到了更好的新量子纠错（QEC）码。对于环上的另一个应用，我们借助循环码的格雷图像得到了几个最优码。
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