Isometrically Self-dual Cyclic Codes
Information Theory
2016-10-05 v1 math.IT
Abstract
General isometries of cyclic codes, including multipliers and translations, are introduced; and isometrically self-dual cyclic codes are defined. In terms of Type-I duadic splittings given by multipliers and translations, a necessary and sufficient condition for the existence of isometrically self-dual cyclic codes is obtained. A program to construct isometrically self-dual cyclic codes is provided, and illustrated by several examples. In particular, a class of isometrically self-dual MDS cyclic codes, which are alternant codes from a class of generalized Reed-Solomon codes, is presented.
Cite
@article{arxiv.1610.00845,
title = {Isometrically Self-dual Cyclic Codes},
author = {Yun Fan and Liang Zhang},
journal= {arXiv preprint arXiv:1610.00845},
year = {2016}
}