Parity check systems of nonlinear codes over finite commutative Frobenius rings
Information Theory
2016-04-26 v1 math.IT
Abstract
The concept of parity check matrices of linear binary codes has been extended by Heden [9] to parity check systems of nonlinear binary codes. In the present paper we extend this concept to parity check systems of nonlinear codes over finite commutative Frobenius rings. Using parity check systems, results on how to get some fundamental properties of the codes are given. Moreover, parity check systems and its connection to characters is investigated and a MacWilliams type theorem on the distance distribution is given.
Keywords
Cite
@article{arxiv.1604.06996,
title = {Parity check systems of nonlinear codes over finite commutative Frobenius rings},
author = {Thomas Westerbäck},
journal= {arXiv preprint arXiv:1604.06996},
year = {2016}
}
Comments
Submitted for publication