Loading...
Codes over a ring of order 32 with two Gray maps
Dougherty, Steven T. Gildea, Joe Korban, Adrian Korban, Adrian Roberts, Adam
Dougherty, Steven T.
Gildea, Joe
Korban, Adrian
Korban, Adrian
Roberts, Adam
Advisors
Editors
Other Contributors
Affiliation
EPub Date
Publication Date
2024-02-09
Submitted Date
Collections
Other Titles
Abstract
We describe a ring of order 32 and prove that it is a local Frobenius ring. We study codes over this ring and we give two distinct non-equivalent linear orthogonality-preserving Gray maps to the binary space. Self-dual codes are studied over this ring as well as the binary self-dual codes that are the Gray images of those codes. Specifically, we show that the image of a self-dual code over this ring is a binary self-dual code with an automorphism consisting of 2n transpositions for the first map and n transpositions for the second map. We relate the shadows of binary codes to additive codes over the ring. As Gray images of codes over the ring, binary self-dual
[
70
,
35
,
12
]
codes with 91 distinct weight enumerators are constructed for the first time in the literature.
Citation
Dougherty, S. T., Gildea, J., Korban, A., & Roberts, A. M. (2024). Codes over a ring of order 32 with two Gray maps. Finite Fields and Their Applications, 95, 102384. https://doi.org/10.1016/j.ffa.2024.102384
Publisher
Elsevier
Journal
Finite Fields and Their Applications
Research Unit
DOI
10.1016/j.ffa.2024.102384
PubMed ID
PubMed Central ID
Type
Article
Language
Description
Series/Report no.
ISSN
1071-5797