An Algebraic Method for Decoding q-ary Codes via Submodules of Z^n
Malihe Aliasgari, Mohammad‐Reza Sadeghi · IEEE Communications Letters · 2014
In this paper, by using a relation between binomial ideal and submodules of Znin , 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.