Reed-muller codes and Barnes-Wall lattices: Generalized multilevel constructions and representation over GF(2 q)

Amir J. Salomon, Ofer Amrani

Research output: Contribution to journalArticlepeer-review

Abstract

Generalized multilevel constructions for binary RM(r,m) codes using projections onto GF(2 q ) are presented. These constructions exploit component codes over GF(2), GF(4),..., GF(2 q ) that are based on shorter Reed-Muller codes and set partitioning using partition chains of length-2 l codes. Using these constructions we derive multilevel constructions for the Barnes-Wall Λ(r,m) family of lattices which also use component codes over GF(2), GF(4),..., GF(2 q ) and set partitioning based on partition chains of length-2 l lattices. These constructions of Reed-Muller codes and Barnes-Wall lattices are readily applicable for their efficient decoding.

Original languageEnglish
Pages (from-to)167-180
Number of pages14
JournalDesigns, Codes, and Cryptography
Volume42
Issue number2
DOIs
StatePublished - Jan 2007

Keywords

  • Additive codes
  • Barnes-Wall lattices
  • Finite-fields
  • Mapping
  • Multilevel
  • Multistage
  • Projection
  • Reed-Muller codes
  • Set partition

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