ACD codes and cyclic codes over Z2Rk

Yadav, A and Sagar, V and Sarma, R (2025) ACD codes and cyclic codes over Z2Rk. In: Computational and Applied Mathematics, 44 (1).

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Abstract

We deal with ACD (additive complementary dual) codes and cyclic codes over the mixed alphabet Z2Rk, where Rk:=Z2y/�yk�, k�2. First, we establish a few criteria for Z2Rk-additive codes to be ACD codes. We also present conditions for separable codes and a class of additive codes (not necessarily separable) over Z2Rk to be ACD codes that are both necessary and sufficient. With the help of a Gray map, binary LCD codes are obtained from Z2Rk-additive codes. Moreover, we describe the generator polynomial of the dual of an additive cyclic code over Z2Rk. Finally, we construct examples of optimal binary codes as the Gray image of certain additive cyclic codes over Z2Rk. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024.

Item Type:	Journal Article
Publication:	Computational and Applied Mathematics
Publisher:	Springer Nature
Additional Information:	The copyright for this article belongs to Springer Nature.
Keywords:	Binary images; Codes (symbols); Image coding; Liquid crystals, 11t71; 94b05; 94b25; 94b60; Additive code; Additive complementary dual code; Cyclic code; Dual codes; LCD Codes; Self-dual codes, Liquid crystal displays
Department/Centre:	Division of Electrical Sciences > Electronic Systems Engineering (Formerly Centre for Electronic Design & Technology)
Date Deposited:	12 Dec 2024 17:20
Last Modified:	12 Dec 2024 17:20
URI:	http://eprints.iisc.ac.in/id/eprint/87007

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