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

Abidin Kaya; Bahattin Yildiz; Irfan Siap

doi:10.1016/j.jfranklin.2013.02.029

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

Abidin Kaya, Bahattin Yildiz, Irfan Siap

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English (US)
Pages (from-to)	751-762
Number of pages	12
Journal	Journal of the Franklin Institute
Volume	351
Issue number	2
DOIs	https://doi.org/10.1016/j.jfranklin.2013.02.029
State	Published - Feb 2014
Externally published	Yes

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Computer Networks and Communications
Applied Mathematics

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10.1016/j.jfranklin.2013.02.029

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abstract = "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+u F2 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.",

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AB - 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+u F2 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.

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

Abstract

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