Composite Matrices from Group Rings, Composite G-Codes and Constructions of Self-Dual Codes
Affiliation
University of Scranton; University of Chester; Harmony School of TechnologyPublication Date
2021-05-19Metadata
Show full item recordAbstract
In this work, we define composite matrices which are derived from group rings. We extend the idea of G-codes to composite G-codes. We show that these codes are ideals in a group ring, where the ring is a finite commutative Frobenius ring and G is an arbitrary finite group. We prove that the dual of a composite G-code is also a composite G-code. We also define quasi-composite G-codes. Additionally, we study generator matrices, which consist of the identity matrices and the composite matrices. Together with the generator matrices, the well known extension method, the neighbour method and its generalization, we find extremal binary self-dual codes of length 68 with new weight enumerators for the rare parameters $\gamma$ = 7; 8 and 9: In particular, we find 49 new such codes. Moreover, we show that the codes we find are inaccessible from other constructions.Citation
Dougherty, S. T., Gildea, J., Korban, A., & Kaya, A. (2021). Composite matrices from group rings, composite G-Codes and constructions of self-dual codes. Designs, Codes and Cryptography, 89, 1615-1638. https://doi.org/10.1007/s10623-021-00882-8Publisher
SpringerJournal
Designs, Codes and CryptographyAdditional Links
https://link.springer.com/article/10.1007/s10623-021-00882-8Type
ArticleDescription
This document is the Accepted Manuscript version of a published work that appeared in final form in Designs, Codes and Cryptography. To access the final edited and published work see http://dx.doi.org/10.1007/s10623-021-00882-8ISSN
0925-1022EISSN
1573-7586Scopus Count
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Except where otherwise noted, this item's license is described as https://creativecommons.org/licenses/by-nc-nd/4.0/
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