Abstract
This paper is devoted to the study of self-dual codes arising from constacyclic codes. Necessary and sufficient conditions are given for the existence of Hermitian self-dual constacyclic codes over \(\mathbb{F }_{q^{2}}\) of length \(n\). As an application of these necessary and sufficient conditions, some conditions under which MDS Hermitian self-orthogonal and self-dual constacyclic codes exist are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aydin N., Siap I., Ray-Chaudhuri D.J.: The structure of 1-generator quasi-twisted codes and new linear codes. Des. Codes Cryptogr. 24(3), 313–326 (2001).
Berlekamp E.R.: Algebraic Coding Theory. McGraw-Hill, New York (1968).
Blackford T.: Negacyclic duadic codes. Finite Fields Appl. 14(4), 930–943 (2008).
Dinh H.Q.: Constacyclic codes of length \(p^{s}\) over \({\mathbb{F}}_{p^{m}}+u{\mathbb{F}}_{p^{m}}\). J. Algebra 324(5), 940–950 (2010).
Guenda K.: New MDS self-dual codes over large finite fields. Des. Codes Cryptogr. 62(1), 31–42 (2011).
Gulliver T.A., Kim J.L., Lee Y.: New MDS or near MDS self-dual codes. IEEE Trans. Inf. Theory 54(9), 4354–4360 (2008).
Huffman W.C., Pless V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, New York (2003).
Jian Y., Ling S., Xing C.: On self-dual cyclic codes over finite fields. IEEE Trans. Inf. Theory 57(4), 2243–2251 (2011).
Kim J.L., Lee Y.: Euclidean and Hermitian self-dual MDS codes over large finite fields. Comb. Theory A 105(1), 79–95 (2004).
Pedersen P., Dahl C.: Classification of pseudo-cyclic MDS codes. IEEE Trans. Inf. Theory 37(2), 365–370 (1991).
Acknowledgments
The authors wish to thank the reviewers for their valuable comments and suggestions which greatly helped us to improve this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by D. Jungnickel.
Rights and permissions
About this article
Cite this article
Yang, Y., Cai, W. On self-dual constacyclic codes over finite fields. Des. Codes Cryptogr. 74, 355–364 (2015). https://doi.org/10.1007/s10623-013-9865-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-013-9865-9