An algebraic method for decoding q-ary codes via submodules of ℤn

Malihe Aliasgari, Mohammad Reza Sadeghi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper, by using a relation between binomial ideal and submodules of ℤn in , a submodule associated with the integer programming (IP) problem is defined. By computing the reduced Gröbner basis (RGB) of the submodule, the decoding problem of non-binary q-ary codes is considered as an integer program problem. Decoding complexity is investigated and the effective factors in complexity are also determined. Furthermore, an example of the decoding method for a 3-ary code is provided.

Original languageEnglish
Article number6777393
Pages (from-to)857-860
Number of pages4
JournalIEEE Communications Letters
Volume18
Issue number5
DOIs
StatePublished - May 2014

Keywords

  • group code
  • Gröbner basis
  • Integer programming
  • ℤ-module

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