Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895652 | Finite Fields and Their Applications | 2018 | 22 Pages |
Abstract
In 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Joe Gildea, Abidin Kaya, Rhian Taylor, Bahattin Yildiz,