Multi-dimensional constacyclic codes of arbitrary length over finite fields

Swati Bhardwaj () and Madhu Raka ()
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Swati Bhardwaj: Panjab University
Madhu Raka: Panjab University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 4, 1485-1498

Abstract: Abstract Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over finite fields. Following the same technique, here we characterize the algebraic structure of multi-dimensional constacyclic codes, in particular three-dimensional $$(\alpha ,\beta ,\gamma )$$ ( α , β , γ ) -constacyclic codes of arbitrary length $$s\ell k$$ s ℓ k and their duals over a finite field $$\mathbb {F}_q$$ F q , where $$\alpha ,\beta ,\gamma $$ α , β , γ are non zero elements of $$\mathbb {F}_q$$ F q . We give necessary and sufficient conditions for a three-dimensional $$(\alpha ,\beta ,\gamma )$$ ( α , β , γ ) -constacyclic code to be self-dual.

Keywords: Cyclic codes; Self-dual; Central primitive idempotents; 94B15; 94B05; 11T71 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00453-8

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