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

07/18/2023

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by   Makoto Araya, et al.

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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.