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

Malihe Aliasgari; Mohammad Reza Sadeghi

doi:10.1109/LCOMM.2014.030914.132773

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

Malihe Aliasgari, Mohammad Reza Sadeghi

New Jersey Center for Science, Technology and Mathematics

Amirkabir University of Technology

Research output: Contribution to journal › Article › peer-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 language	English
Article number	6777393
Pages (from-to)	857-860
Number of pages	4
Journal	IEEE Communications Letters
Volume	18
Issue number	5
DOIs	https://doi.org/10.1109/LCOMM.2014.030914.132773
State	Published - May 2014

Keywords

Gröbner basis
Integer programming
group code
ℤ-module

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10.1109/LCOMM.2014.030914.132773

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AB - 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.

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

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