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

In this work, the main purpose is to extend some well known binary and quaternary codes to the ring F2+uF2. 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 F2+uF2 are also obtained. As an application of this extension, we also present a new algebraic method of obtaining polar codes from codes over F2+uF2. 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.