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AbstractWe 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.
CitationDougherty, 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
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