Isometrically Self-dual Cyclic Codes

Yun Fan; Liang Zhang

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arXiv · 1610.00845

Isometrically Self-dual Cyclic Codes

Yun Fan·Liang Zhang

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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.

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Yun Fan, Liang Zhang. 2016-10-04. Isometrically Self-dual Cyclic Codes. https://arxiv.org/abs/1610.00845

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