QUASI-CYCLIC SELF-DUAL CODES WITH FOUR FACTORS

Hyun Jin Kim; Whan Hyuk Choi; Jung Kyung Lee

doi:10.11568/kjm.2024.32.3.485

QUASI-CYCLIC SELF-DUAL CODES WITH FOUR FACTORS

Hyun Jin Kim, Whan Hyuk Choi, Jung Kyung Lee

University College

Research output: Contribution to journal › Article › peer-review

Abstract

In this study, we examine ℓ-quasi-cyclic self-dual codes of length ℓm over F₂, provided that the polynomial X^m − 1 has exactly four distinct irreducible factors in F₂[X]. We find the standard form of generator matrices of codes over the ring R^∼= F_q [X]/(X^m − 1) and the conditions for the codes to be self-dual. We explicitly determine the forms of generator matrices of self-dual codes of lengths 2 and 4 over R.

Original language	English
Pages (from-to)	485-496
Number of pages	12
Journal	Korean Journal of Mathematics
Volume	32
Issue number	3
DOIs	https://doi.org/10.11568/kjm.2024.32.3.485
Publication status	Published - 2024 Sept 30

Bibliographical note

Publisher Copyright:
© The Kangwon-Kyungki Mathematical Society, 2024.

All Science Journal Classification (ASJC) codes

General Mathematics

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10.11568/kjm.2024.32.3.485

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title = "QUASI-CYCLIC SELF-DUAL CODES WITH FOUR FACTORS",

abstract = "In this study, we examine ℓ-quasi-cyclic self-dual codes of length ℓm over F2, provided that the polynomial Xm − 1 has exactly four distinct irreducible factors in F2[X]. We find the standard form of generator matrices of codes over the ring R∼= Fq [X]/(Xm − 1) and the conditions for the codes to be self-dual. We explicitly determine the forms of generator matrices of self-dual codes of lengths 2 and 4 over R.",

keywords = "automorphism, linear codes, quasi-cyclic code, reciprocal polynomials, self-dual code",

author = "Kim, {Hyun Jin} and Choi, {Whan Hyuk} and Lee, {Jung Kyung}",

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doi = "10.11568/kjm.2024.32.3.485",

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T1 - QUASI-CYCLIC SELF-DUAL CODES WITH FOUR FACTORS

AU - Kim, Hyun Jin

AU - Choi, Whan Hyuk

AU - Lee, Jung Kyung

N1 - Publisher Copyright: © The Kangwon-Kyungki Mathematical Society, 2024.

PY - 2024/9/30

Y1 - 2024/9/30

N2 - In this study, we examine ℓ-quasi-cyclic self-dual codes of length ℓm over F2, provided that the polynomial Xm − 1 has exactly four distinct irreducible factors in F2[X]. We find the standard form of generator matrices of codes over the ring R∼= Fq [X]/(Xm − 1) and the conditions for the codes to be self-dual. We explicitly determine the forms of generator matrices of self-dual codes of lengths 2 and 4 over R.

AB - In this study, we examine ℓ-quasi-cyclic self-dual codes of length ℓm over F2, provided that the polynomial Xm − 1 has exactly four distinct irreducible factors in F2[X]. We find the standard form of generator matrices of codes over the ring R∼= Fq [X]/(Xm − 1) and the conditions for the codes to be self-dual. We explicitly determine the forms of generator matrices of self-dual codes of lengths 2 and 4 over R.

KW - automorphism

KW - linear codes

KW - quasi-cyclic code

KW - reciprocal polynomials

KW - self-dual code

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AN - SCOPUS:85206574159

SN - 1976-8605

VL - 32

SP - 485

EP - 496

JO - Korean Journal of Mathematics

JF - Korean Journal of Mathematics

IS - 3

ER -

QUASI-CYCLIC SELF-DUAL CODES WITH FOUR FACTORS

Abstract

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