Some new constructions of isodual and LCD codes over finite fields

Fatma-Zohra Benahmed; Kenza Guenda; Aicha Batoul; Thomas Aaron Gulliver

doi:10.3934/amc.2019019

Article Contents

2019, Volume 13, Issue 2: 281-296. Doi: 10.3934/amc.2019019

This issue Previous Article Some classes of LCD codes and self-orthogonal codes over finite fields Next Article Further results on optimal $ (n, \{3, 4, 5\}, \Lambda_a, 1, Q) $-OOCs

Some new constructions of isodual and LCD codes over finite fields

1.
University M'Hamed Bougara of Boumerdes, Faculty of Sciences, Boumerdes, Algeria
2.
University of Science and Technology: Houari Boumediene, Faculty of Mathematics, Algiers, 16411, Algeria
3.
Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC V8W 2Y2, Canada

^* Corresponding author: Aicha Batoul
^* Corresponding author: Aicha Batoul

Received: April 2018

Revised: August 2018

Published: January 2019

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Abstract

This paper presents some new constructions of LCD, isodual, self-dual and LCD-isodual codes based on the structure of repeated-root constacyclic codes. We first characterize repeated-root constacyclic codes in terms of their generator polynomials and lengths. Then we provide simple conditions on the existence of repeated-root codes which are either self-dual negacyclic or LCD cyclic and negacyclic. This leads to the construction of LCD, self-dual, isodual, and LCD-isodual cyclic and negacyclic codes.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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