Abstract
In this paper, we introduce \(\omega\)-constacyclic Type II duadic codes over \({\mathbb {F}}_4\) of length \(n=3p^t\), where p is a prime number, \(p \equiv 1\) (mod 6), and give their main properties. We also obtain a splitting of n such that extended \(\omega\)-constacyclic duadic codes are Hermitian self-dual. Moreover, we provide some examples by extended \(\omega\)-constacyclic duadic codes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blackford, T.: Negacyclic duadic codes. Finite Fields Appl. 14, 930–943 (2008)
Blackford, T.: Isodual constacyclic codes. Finite Fields Appl. 24, 29–44 (2013)
Fan, Y., Zhang, L.: Galois self-dual constacyclic codes. Des. Codes Cryptogr. 84, 473–492 (2017)
Grassl, M., Gulliver, T.A.: On circulant self-dual codes over small fields. Des. Codes Cryptogr. 52, 57–81 (2009)
Huffman, W.C., Pless, V.: Fundamentals of Error Correcting Codes. Cambrigde University Press, Cambrigde (2003)
Huffman, W.C.: On the classification and enumeration of self-dual codes. Finite Fields Appl. 11, 451–490 (2005)
Leon, J.S., Masley, J.M., Pless, V.: Duadic codes. IEEE Trans. Inf. Theory 30, 709–714 (1984)
Yang, Y., Cai, W.: On self-dual constacyclic codes over finite fields. Des. Codes Cryptogr. 74, 355–364 (2011)
Acknowledgements
The authors thank the anonymous referees for their valuable comments, which enabled them to improve the quality of the paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Karbaski, A.S., Samei, K. & Sepahvand, T. Constacyclic duadic codes over \({\mathbb {F}}_4\). AAECC 34, 267–277 (2023). https://doi.org/10.1007/s00200-021-00502-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00200-021-00502-x