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Open Access Research Article

Idempotent generators of cyclic codes, cyclic self-dual codes and cyclic LCD codes of length ptq over ℤ4

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pp. 2769–2796Vol. 28Issue 7October 2025DOI: 10.47974/JDMSC-2116 Crossmark XML
Received:
05 Dec 2023
Published Online:
26 Feb 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2116
Pages:
2769–2796

Abstract

Cyclic codes having length ptq have been studied using the primitive binary idempotent generators when Opt(2) = f(pt)/2  and Oq(2) = q – 1  with (f(pt)/2, q – 1).  Using the expressions of these idempotent generators and the theory of cyclotomy, expressions of idempotent generators of ℤ4 – cyclic codes are obtained. In this case, all the self-dual codes and LCD codes of length ptq  over ℤ4 are defined in terms of the idempotent generators. Clearly, these self-dual cyclic codes of length ptq are Type-I codes. Also, the permutational equivalence of these cyclic codes has been discussed.

Keywords

Subject Classifications

94B1511T7116S34

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