Codes over a ring of order 32 with two Gray maps

• Published in: Finite fields and their applications 2024-03, Vol.95, p.102384, Article 102384
• Main Authors: Dougherty, S.T., Gildea, J., Korban, A., Roberts, A.M.
• Format: Article
• Language: English
• Subjects: Best known; Codes over rings; Extremal codes; Gray maps; Self-dual codes
• ISSN: 1071-5797; 1090-2465
• DOI: 10.1016/j.ffa.2024.102384

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.