Title: Self-dual codes over Z₄[x]/(x² + 2x) and the Z₄-images

Authors: Bahattin Yildiz; Abidin Kaya

Addresses: Department of Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ 86004, USA ' Sampoerna Academy, L'Avenue Campus, 12780, Jakarta, Indonesia

Abstract: In this work, constructions for self-dual codes over the ring Z₄[x]/(x² + 2x) are considered together with their images under an orthogonality-preserving grey map, which result in self-dual Z4-codes. Theoretical results about the existence/non-existence of self-dual codes from construction methods such as the double circulant, bordered double circulant and four circulant matrices for the rings Z₄ and Z₄[x]/(x² + 2x) are given. The construction methods are then applied to get good self-dual Z₄-codes of lengths 16, 32, 48 and 64 (including some extremal type I and type II codes), which are tabulated at the end.

Keywords: self-dual codes; codes over rings; grey maps; double-circulant codes; bordered double circulant codes; four circulant codes.

DOI: 10.1504/IJICOT.2018.095016

International Journal of Information and Coding Theory, 2018 Vol.5 No.2, pp.142 - 154

Received: 27 Jun 2018
Accepted: 17 Jul 2018
Published online: 28 Sep 2018 *

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