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arXiv · 2003.05296

New Extremal Binary Self-Dual Codes from Block Circulant Matrices and Block Quadratic Residue Circulant Matrices

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

In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2 and F2 + uF2. Using extensions, neighbours and sequences of neighbours, we construct many new self-dual codes. In particular, we construct one new self-dual code of length 66 and 51 new self-dual codes of length 68.

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Joe Gildea, Abidin Kaya, Rhian Taylor, Alexander Tylyshchak, Bahattin Yildiz. 2020-03-10. New Extremal Binary Self-Dual Codes from Block Circulant Matrices and Block Quadratic Residue Circulant Matrices. https://arxiv.org/abs/2003.05296

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