On the structure of repeated-root polycyclic codes over local rings

Authors

Maryam Bajalan, Bulgarian Academy of Sciences
Edgar Martinez-Moro, University of Valladolid
Reza Sobhani, University of Isfahan
Steve Szabo, Eastern Kentucky UniversityFollow
Gulsum Gozde Yilmazguc, Trakya University

Author ORCID Identifier

• https://orcid.org/0000-0002-0523-5162View this author’s ORCID profile

Department

Mathematics and Statistics

Department Name When Scholarship Produced

Mathematics and Statistics

Document Type

Article

Publication Date

1-2024

Abstract

This paper provides the Generalized Mattson Solomon polynomial for repeated-root polycyclic codes over local rings that gives an explicit decomposition of them in terms of idempotents. It also states some structural properties of repeated-root polycyclic codes over finite fields in terms of matrix product codes. Both approaches provide a description of the -dual code for a given polycyclic code.

Recommended Citation

Bajalan, M., Martínez-Moro, E., Sobhani, R., Szabo, S., & Yılmazgüç, G. G. (2024). On the structure of repeated-root polycyclic codes over local rings. Discrete Mathematics, 347(1).

Journal Title

Discrete Mathematics