Computing generating sets for quaternary codes using Gröbner bases
International Journal of Pure and Applied Mathematics 1 (84): 99-109 (2013)
Gröbner bases techniques can be used to compute a basis of a subspace of a finite-dimensional vector space over finite prime field given as a matrix kernel. Linear codes can be described as such subspaces and thus are an interesting area of application. Based on this, Gröbner bases techniques will be used to compute a generating set of a quaternary code given as a matrix kernel. In particular, if the quaternary code is free, the algorithm will provide a basis for the dual code.