1-Generator two-dimensional quasi-cyclic codes over ${\mathbb{Z}_4[u]}{\langle u^2-1\rangle}$
DOI:
https://doi.org/10.13069/jacodesmath.1056624Keywords:
Two-dimensional cyclic codes, Two-dimensional quasi-cyclic codes, Two-dimensional generalized quasi-cyclic codesAbstract
In this paper, we obtain generating set of polynomials of two-dimensional cyclic codes over the ring $R=\mathbb{Z}_4[u]/\langle u^2-1\rangle$, where $u^2=1$. Moreover, we find generator polynomials for two-dimensional quasi-cyclic codes and two-dimensional generalized quasi-cyclic codes over $R$ and specify a lower bound on minimum distance of free 1-generator two-dimensional quasi-cyclic codes and two-dimensional generalized quasi-cyclic codes over $R$.
Received: 11 July 2021 | Accepted: 8 October 2021Downloads
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Published
2022-01-13
How to Cite
Ghajari, A. ., Khashyarmanesh, K. ., & Rajabi, Z. . (2022). 1-Generator two-dimensional quasi-cyclic codes over ${\mathbb{Z}_4[u]}{\langle u^2-1\rangle}$. Journal of Algebra Combinatorics Discrete Structures and Applications, 9(1), 57–70. https://doi.org/10.13069/jacodesmath.1056624
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