Title: Linear transformation codes: codes with a compact description and transpoliser codes

Authors: Steven Dougherty; Bahattin Yildiz

Addresses: Department of Mathematics, University of Scranton, Scranton, PA, USA ' Department of Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ, USA

Abstract: In this paper we define linear transformation codes, which provides a compact description to traditional codes. We divide them into ideal codes and multiplicative codes and show that the multiplicative codes are the more useful of the two. We relate them to linear and additive codes over non-commutative rings and show how to use the canonical orthogonals in each case to construct new codes. Extending on the specific examples of centraliser and twisted centraliser codes, we define a new family of codes, which we call transpoliser codes, that can be defined over the binary field without the restrictive upper bound on the minimum distance.

Keywords: linear transformation codes; matrices; transpoliser codes; centraliser codes; Frobenius rings.

DOI: 10.1504/IJICOT.2020.110707

International Journal of Information and Coding Theory, 2020 Vol.5 No.3/4, pp.185 - 197

Received: 05 Aug 2019
Accepted: 08 Mar 2020

Published online: 13 Oct 2020 *

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