On Reed-Muller codes over F2 + uF2 and some applications

Abstract

In this work, the main purpose is to extend some well known binary and quaternary codes to the ring F-2 + uF(2). Reed Muller, Goethals, Delsarte-Goethals codes are extended, their properties and relations to binary and quaternary versions are studied. Double error correcting families of codes as Goethals and shortened Goethals codes over F-2 + uF(2) are also obtained. As an application of this extension, we also present a new algebraic method of obtaining polar codes from codes over F-2 + uF(2). We introduce two new polar-like codes from codes over this ring, which we call RM1 and RM2 codes. Finally polar codes for the binary erasure channel (BEC) and Reed Muller codes are compared in terms of trellis complexity. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.