Composite constructions of self-dual codes from group rings and new extremal self-dual binary codes of length 68

Abstract

We describe eight composite constructions from group rings where the orders of the groups are 4 and 8, which are then applied to find self-dual codes of length 16 over F4 . These codes have binary images with parameters [32, 16, 8] or [32, 16, 6]. These are lifted to codes over F4 + uF4, to obtain codes with Gray images of extremal self-dual binary codes of length 64. Finally, we use a building-up method over F2 +uF2 to obtain new extremal binary self-dual codes of length 68. We construct 11 new codes via the building-up method and 2 new codes by considering possible neighbors.