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 𝔽q. Let ℛ = 𝔽q[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 (𝔽q 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.
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: 14 May 2018 *