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

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dc.contributor.authorKaya, Abidin
dc.contributor.authorYildiz, Bahattin
dc.contributor.authorSiap, Irfan
dc.date.accessioned2026-06-27T13:29:29Z
dc.date.issued2014
dc.description.abstractIn 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.en
dc.description.urihttps://doi.org/10.1016/j.jfranklin.2013.02.029
dc.identifier.doi10.1016/j.jfranklin.2013.02.029
dc.identifier.eissn1879-2693
dc.identifier.endpage762
dc.identifier.issn0016-0032
dc.identifier.issue2
dc.identifier.startpage751
dc.identifier.urihttps://hdl.handle.net/20.500.14981/53154
dc.identifier.volume351
dc.identifier.wos000329972500013
dc.language.isoeng
dc.publisherPERGAMON-ELSEVIER SCIENCE LTD
dc.relation.conferenceInternational Conference on Applied Analysis and Algebra (ICAAA)
dc.relation.ispartofJOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
dc.subjectSELF-DUAL CODES
dc.subjectCYCLIC CODES
dc.subjectPOLAR CODES
dc.subjectAutomation & Control Systems
dc.subjectEngineering
dc.subjectMathematics
dc.titleOn Reed-Muller codes over F2 + uF2 and some applications
dc.typeArticle; Proceedings Paper
dspace.entity.typePublication
local.import.sourceWOS

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