New extremal self-dual binary codes of length 68 via composite construction, \( \mathbb{F}_2 + u \mathbb{F}_2\) lifts, extensions and neighbours
type: Item
instance of: scholarly article
title: New extremal self-dual binary codes of length 68 via composite construction, \( \mathbb{F}_2 + u \mathbb{F}_2\) lifts, extensions and neighbours
zbMATH Open document ID: 1485.94155
DOI: 10.1504/IJICOT.2020.110703
author: Steven T. Dougherty
author: Joe Gildea
author: Adrian Korban
author: Abidin Kaya
published in: International Journal of Information and Coding Theory
publication date: 2021-05-04T00:00:00Z
review text: Summary: 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 \(\mathbb{F}_2 + u \mathbb{F}_2\), 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.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 7343542
zbMATH Keywords: group rings
zbMATH Keywords: self-dual codes
zbMATH Keywords: codes over rings
MaRDI profile type: Publication
full work available at URL: ijicot.2020.110703
OpenAlex ID: W3097352577
description: scientific article; zbMATH DE number 7343542