Hadamard matrices of orders 60 and 64 with automorphisms of orders 29 and 31

Makoto Araya; Masaaki Harada; Vladimir D. Tonchev

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arXiv · 2307.08983

Hadamard matrices of orders 60 and 64 with automorphisms of orders 29 and 31

Makoto Araya·Masaaki Harada·Vladimir D. Tonchev

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Abstract

A classification of Hadamard matrices of order $2p+2$ with an automorphism of order $p$ is given for $p=29$ and $31$. The ternary self-dual codes spanned by the newly found Hadamard matrices of order $60$ with an automorphism of order $29$ are computed, as well as the binary doubly even self-dual codes of length $120$ with generator matrices defined by related Hadamard designs. Several new ternary near-extremal self-dual codes, as well as binary near-extremal doubly even self-dual codes with previously unknown weight enumerators are found.

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Makoto Araya, Masaaki Harada, Vladimir D. Tonchev. 2023-07-18. Hadamard matrices of orders 60 and 64 with automorphisms of orders 29 and 31. https://arxiv.org/abs/2307.08983

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