AffiliationUniversity of Chester; Sampoerna Academy, University of Chester; Northern Arizona University
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AbstractIn this work, we establish a strong connection between group rings and self-dual codes. We prove that a group ring element corresponds to a self-dual code if and only if it is a unitary unit. We also show that the double-circulant and four-circulant constructions come from cyclic and dihedral groups, respectively. Using groups of order 8 and 16 we find many new construction methods, in addition to the well-known methods, for self-dual codes. We establish the relevance of these new constructions by finding many extremal binary self-dual codes using them, which we list in several tables. In particular, we construct 10 new extremal binary self-dual codes of length 68.
CitationGildea, J., Kaya, A., Taylor, R., & Yildiz, B. (2018). Constructions for Self-Dual Codes Induced from Group Rings, to appear in Finite Fields and Their Applications, 51, 71-92. https://doi.org/10.1016/j.ffa.2018.01.002
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