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A STUDY OF SKEW CONSTACYCLIC CODES OVER $Z_4+u\mathbb{Z}_4 (u^2=2)$
Keywords:
cyclic code, constacyclic code, quasi-cyclic code, Gray mapAbstract
In this article, we study skew $\theta - (1+2u)$-constacyclic codes over $R=\mathbb{Z}_4+u\mathbb{Z}_4,$ where $u^2=2$ and define some new Gray maps from $\mathbb{Z}_4+u\mathbb{Z}_4$ to $\mathbb{Z}_4$ and $\mathbb{F}_4$. It is shown that the Gray images of skew $\theta - (1+2u)$-constacyclic codes over $\mathbb{Z}_4+u\mathbb{Z}_4$ are cyclic over $\mathbb{Z}_4$ of length $2n$, and are quasi-cyclic and permutation equivalent to quasi-cyclic codes over $\mathbb{F}_2$ of length $4n$.
Received: January 2, 2023
Accepted: February 4, 2023
References
E. Prange, Cyclic error-correcting codes in two symbols, Air Force Cambridge Research Center-TN-57-103, Cambridge, MA, 1957.
E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill Book Company, New York, 1968.
D. Boucher, W. Geiselmann and F. Ulmer, Skew-cyclic codes, Appl. Algebra Engrg. Comm. Comput. 18 (2007), 379-389.
D. Boucher, P. Sole and F. Ulmer, Skew-constacyclic codes over Galois ring, Adv. Math. Commun. 2(3) (2008), 273-292.
R. K. Bandi and M. Bhaintwal, A note on cyclic codes over Discrete Mathematics, Algorithms and Applications 8(1) (2016), 17 pages, 1650017.
Tushar Bag, Habibul Islam, Om Prakash and Ashish K. Upadhyay, A study of constacyclic codes over the ring Discrete Mathematics, Algorithms and Applications 10(4) (2018), 10 pages, 1850056.
Amit Sharma and Maheshanand Bhaintwal, A class of skew-constacyclic codes over Int. J. Information and Coding Theory 4(4) (2017), 289-303.
T. Abualrub and I. Siap, Reversible cyclic codes over Australas. J. Combin. 38 (2007), 195-206.
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