Title: New extremal self-dual binary codes of length 68 via composite construction, 𝔽2 + u𝔽2 lifts, extensions and neighbours

Authors: Steven T. Dougherty; Joe Gildea; Adrian Korban; Abidin Kaya

Addresses: Department of Mathematics, University of Scranton, Scranton, PA 18510, USA ' Department of Mathematical and Physical Sciences, University of Chester, Thornton Science Park, Pool Ln, Chester CH2 4NU, England, UK ' Department of Mathematical and Physical Sciences, University of Chester, Thornton Science Park, Pool Ln, Chester CH2 4NU, England, UK ' Department of Engineering Fundamentals, Sampoerna University, 12780, Jakarta, Indonesia

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 + u𝔽2, 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.

Keywords: group rings; self-dual codes; codes over rings.

DOI: 10.1504/IJICOT.2020.110703

International Journal of Information and Coding Theory, 2020 Vol.5 No.3/4, pp.211 - 226

Received: 05 Oct 2019
Accepted: 29 Feb 2020

Published online: 13 Oct 2020 *

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