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Two dimensional double cyclic codes over finite fields

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Abstract

A linear code C of length \(n = ru + sv\) is a two-dimensional \({\mathbb {F}}\)-double cyclic code if the set of coordinates can be partitioned into two arrays, such that any cyclic row-shifts and column-shifts of both arrays of a codeword is also a codeword. In this paper, we examine the algebraic structure of these codes and their dual codes in general. Moreover, we are interested in finding out a generating set for these codes (and their dual codes) in case when \(u=2\), \(v=4\) and char\((F) \ne 2\).

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Acknowledgements

The authors are deeply grateful to the referees for careful reading of the manuscript and helpful suggestions.

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  1. Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran

    Niloufar Hajiaghajanpour & Kazem Khashyarmanesh

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  1. Niloufar Hajiaghajanpour
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  2. Kazem Khashyarmanesh
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Correspondence to Kazem Khashyarmanesh.

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Hajiaghajanpour, N., Khashyarmanesh, K. Two dimensional double cyclic codes over finite fields. AAECC (2023). https://doi.org/10.1007/s00200-023-00595-6

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