New extremal self-dual binary codes of length 68 via composite construction, 𝔽2 + u𝔽2 lifts, extensions and neighbours. (13th October 2020)

• Record Type: Journal Article
• Authors: Dougherty, Steven T.; Gildea, Joe; Korban, Adrian; Kaya, Abidin
• Is Part Of: International journal of information and coding theory. Volume 5:Number 3/4(2020)
• Page Start: 211
• Page End: 226
• Publication Date: 2020-10-13
• Subjects: group rings -- self-dual codes -- codes over rings; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

Abstract

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 𝔽2 + u 𝔽2, 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.