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Research Article | Open Access

Double circulant complementary dual codes over F 4

Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
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Abstract

Linear codes with complementary-duals (LCD codes) are linear codes that trivially intersect with their dual (Massey, 1992). In this paper, we study double circulant codes (DC codes), which are a special class of quasi-cyclic codes, over F 4 that are LCD. The main techniques used are as follows: Chinese reminder theory (CRT) decomposition in the line of (Ling et al. 2001), explicit enumeration, and asymptotics. In particular, we show that the class of codes considered here is asymptotically good.

Keywords

Artin's conjecturedouble circulant codeLCD codes
CLC number: 94B15

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 21636-21643
DOI: 10.3934/math.20231103

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Cite this article:
Shoaib H. Double circulant complementary dual codes over F 4 . AIMS Mathematics, 2023, 8(9): 21636-21643. https://doi.org/10.3934/math.20231103

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Received: 01 May 2023
Revised: 24 June 2023
Accepted: 28 June 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)