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A construction of a jacket matrix motivated by the element inverse property of the centre weighted Hadamard matrix is presented with suitably chosen characters on a finite Abelian group. The present matrix, which is an extension of the conventional jacket matrices on the Galois field, is a contribution to a problem of searching for an extended family of jacket matrices on finite Abelian group.
A modification of the classical Hadamard matrices is presented, which is defined over the fields of finite characteristic. The issue for the existence (necessary conditions) of odd order matrices of that kind is addressed. An application to cryptography of the corresponding linear transforms is pointed out.
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