Quadruple bordered constructions of self-dual codes from group rings

• DOI: 10.1007/s12095-019-00380-8
• Publication Date: 2019-07-05T02:02:37Z
• Authors: Steven T. Dougherty; Joseph Gildea; Abidin Kaya
• Keywords: self-dual codes; extremal codes; codes over rings; bordered constructions; 0202 electrical engineering, electronic engineering, information engineering; group rings; 02 engineering and technology

In this paper, we introduce a new bordered construction for self-dual codes using group rings. We consider constructions over the binary field, the family of rings Rk and the ring $\mathbb {F}_{4}+u\mathbb {F}_{4}$. We use groups of order 4, 12 and 20. We construct some extremal self-dual codes and non-extremal self-dual codes of length 16, 32, 48, 64 and 68. In particular, we construct 33 new extremal self-dual codes of length 68.