Title: Duadic and triadic codes over a finite non-chain ring and their Gray images

Authors: Mokshi Goyal; Madhu Raka

Addresses: Centre for Advanced Study in Mathematics, Panjab University, Chandigarh-160014, India ' Centre for Advanced Study in Mathematics, Panjab University, Chandigarh-160014, India

Abstract: Let f(u) be a polynomial of degree m, m ≥ 2, which splits into distinct linear factors over a finite field 𝔽_q. Let ℛ = 𝔽_q[u] / ⟨ f(u) ⟩ be a finite non-chain ring. In this paper, we study duadic codes, their extensions and triadic codes over the ring ℛ. A Gray map from ℛⁿ to (𝔽_q ^m)ⁿ is defined which preserves self-duality of linear codes. As a consequence, self-dual, isodual, self-orthogonal and complementary dual(LCD) codes over 𝔽 _q are constructed. Some examples are also given to illustrate this.

Keywords: quadratic residue codes; duadic codes; extended duadic-codes; triadic codes; Gray map; self-dual and self-orthogonal codes; isodual codes; LCD codes.

DOI: 10.1504/IJICOT.2018.091834

International Journal of Information and Coding Theory, 2018 Vol.5 No.1, pp.36 - 54

Received: 20 Jul 2017
Accepted: 26 Nov 2017
Published online: 18 May 2018 *