New extremal self-dual binary codes of length 68 via composite construction, 𝔽₂ + u𝔽₂ lifts, extensions and neighbours
by Steven T. Dougherty; Joe Gildea; Adrian Korban; Abidin Kaya
International Journal of Information and Coding Theory (IJICOT), Vol. 5, No. 3/4, 2020

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.

Online publication date: Wed, 28-Oct-2020

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