Generalized multilevel constructions for Reed-Muller codes and Barnes-Wall lattices

Amir J. Salomon, Ofer Amrani

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Generalized multilevel constructions for binary Reed-Muller R(r, m) codes using projections onto GF (2q) are presented. These constructions exploit component codes over GF(2), GF(4), . . . ,GF(2q) that are based on shorter Reed-Muller codes, and set partitioning using partition chains of length-2l codes. This is then used for deriving multilevel constructions for the Barnes-Wall Λ(r, m) family of lattices. Similarly, the latter construction involves component codes over GF(2), GF(4),. . . ,GF(2q) and set partitioning based on partition chains of length-2l lattices. These constructions of Reed-Muller codes and Barnes-Wall lattices are readily applicable for their efficient decoding.

Original languageEnglish
Title of host publicationProceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Pages896-900
Number of pages5
DOIs
StatePublished - 2006
Event2006 IEEE International Symposium on Information Theory, ISIT 2006 - Seattle, WA, United States
Duration: 9 Jul 200614 Jul 2006

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8101

Conference

Conference2006 IEEE International Symposium on Information Theory, ISIT 2006
Country/TerritoryUnited States
CitySeattle, WA
Period9/07/0614/07/06

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