Title: Repeated-root bidimensional (μ, ν)-constacyclic codes of length 4p^t.2^r

Authors: Shikha Patel; Om Prakash

Addresses: Department of Mathematics, Indian Institute of Technology Patna, Patna-801106, India ' Department of Mathematics, Indian Institute of Technology Patna, Patna-801106, India

Abstract: Let p be an odd prime. The main concern of this article is to study all the repeated-root bidimensional (μ, ν)-constacyclic codes of length 4p^t.2^r over the finite field 𝔽_p^m. Here, we provide all the self-dual repeated-root bidimensional (1, 1)-constacyclic and (−1, 1)-constacyclic codes of length 4p^t.2^r over 𝔽_p^m. We also discuss the repeated-root bidimensional (η, 1)-constacyclic codes of length 4p^t.2^r over 𝔽_p^m. Moreover, it has been shown that these structures are useful in the construction of linear complementary dual (LCD) codes and self-dual codes. As an example, we are listed all the repeated-root bidimensional (μ, ν)-constacyclic codes of length 72 over the finite field 𝔽₂₇.

Keywords: cyclic codes; constacyclic codes; two-dimensional constacyclic codes; dual codes; LCD codes; repeated-root codes.

DOI: 10.1504/IJICOT.2020.110738

International Journal of Information and Coding Theory, 2020 Vol.5 No.3/4, pp.266 - 289

Received: 11 May 2020
Accepted: 26 May 2020
Published online: 28 Oct 2020 *

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