Abstract
For an integer m ≥ 1, we study cyclic codes of length l over a commutative non-chain ring F2m + uF2m , where u2 = u . With a new Gray map and Euclidean dual-containing cyclic codes, we provide many new and superior codes to the best-known quantum error-correcting codes. Also, we characterise LCD codes of length l with respect to their generator polynomials and prove that F2m − image of an LCD code of length l is an LCD code of length 2l . Finally, we provide several optimal LCD codes from the Gray images of LCD codes over F2m + uF2m .
Publisher
Defence Scientific Information and Documentation Centre
Subject
Electrical and Electronic Engineering,Computer Science Applications,General Physics and Astronomy,Mechanical Engineering,Biomedical Engineering,General Chemical Engineering
Cited by
11 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Hermitian hull of constacyclic codes over a class of non-chain rings and new quantum codes;Computational and Applied Mathematics;2024-06-04
2. On quantum and LCD codes from the cyclic codes over the ring $$\mathbb {F}_q[\textsf{u}, \textsf{v},\textsf{w}]/\langle \textsf{u}^3-\textsf{u},\textsf{v}^2-\textsf{v}, \textsf{w}^2-\textsf{w}, \textsf{u}\textsf{v}, \textsf{v}\textsf{u}, \textsf{u}\textsf{w}, \textsf{w}\textsf{u}, \textsf{v}\textsf{w}-\textsf{w}\textsf{v} \rangle $$;Journal of Applied Mathematics and Computing;2024-02-17
3. Cyclic codes over non-chain ring $ \mathcal{R}(\alpha_1, \alpha_2, \ldots, \alpha_s) $ and their applications to quantum and DNA codes;AIMS Mathematics;2024
4. Quantum Codes Over an Extension of $${\mathbb {Z}_4}$$;Springer Proceedings in Mathematics & Statistics;2024
5. Complementary dual skew polycyclic codes and their applications to EAQECCs;The European Physical Journal Plus;2023-07-21