New extremal self-dual binary codes of length 68 via composite construction, \( \mathbb{F}_2 + u \mathbb{F}_2\) lifts, extensions and neighbours
Summary: We describe a composite construction from group rings where the groups have orders 16 and 8. This construction is then applied to find the extremal binary self-dual codes with parameters \([32, 16, 8]\) or \([32, 16, 6]\). We also extend this composite construction by expanding the search field which enables us to find more extremal binary self-dual codes with the above parameters and with different orders of automorphism groups. These codes are then lifted to \(\mathbb{F}_2 + u \mathbb{F}_2\), to obtain extremal binary images of codes of length 64. Finally, we use the extension method and neighbour construction to obtain new extremal binary self-dual codes of length 68. As a result, we obtain 28 new codes of length 68 which were not known in the literature before.
scientific article; zbMATH DE number 7343542