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arXiv · 2002.09789

New Self-Dual Codes from 2x2 Block Circulant Matrices, Group Rings and Neighbours of Neighbours

Joe Gildea·Abidin Kaya·Rhian Taylor·Alexander Tylyshchak
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Abstract

In this paper, we construct self-dual codes from a construction that involves 2x2 block circulant matrices, group rings and a reverse circulant matrix. We provide conditions whereby this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2, F2 + uF2 and F4 + uF4. Using extensions, neighbours and neighbours of neighbours, we construct 32 new self-dual codes of length 68.

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Joe Gildea, Abidin Kaya, Rhian Taylor, Alexander Tylyshchak. 2020-02-22. New Self-Dual Codes from 2x2 Block Circulant Matrices, Group Rings and Neighbours of Neighbours. https://arxiv.org/abs/2002.09789

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