Abstract
Linear codes with additional algebraic structures such as cyclic codes, negacyclic codes and abelian codes have become of interest due to their nice algebraic structures, wide applications and links with other mathematical objects. In this paper, a generalization of negacyclic codes is introduced and studied. Algebraic structures of such codes are given though cyclotomic classes of abelian groups and ideals in twisted group algebras. Recursive constructions and enumerations of such codes are presented. Characterizations of self-dual generalized negacyclic codes and complementary dual generalized negacyclic codes are given as well as their enumerations.
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Acknowledgements
The authors would like to thank the anonymous referees for helpful comments and suggestions. S. Jitman is funded by National Research Council of Thailand and Silpakorn University under Research Grant N42A650381. The research of S. Ling is partially supported by Nanyang Technological University Research Grant No. 04INS000047C230GRT01. J. Tharnnukhroh’s scholarship is from the Development and Promotion of Science and Technology Talent Project, Thailand.
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Jitman, S., Ling, S. & Tharnnukhroh, J. Generalized negacyclic codes over finite fields. J. Appl. Math. Comput. 69, 421–449 (2023). https://doi.org/10.1007/s12190-022-01753-8
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DOI: https://doi.org/10.1007/s12190-022-01753-8
Keywords
- Cyclotomic Classes
- Negacyclic Codes
- Constabelian Codes
- Generalized Negacyclic Codes
- Self-Dual Codes
- Complementary Dual Codes