Emergent Mind
Hadamard matrices of orders 60 and 64 with automorphisms of orders 29 and 31
(2307.08983)
Published Jul 18, 2023
in
math.CO
,
cs.IT
,
and
math.IT
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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