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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.
Lee and colleagues have introduced a generalised reverse jacket transform (GRJT) as a multi-phase or multilevel generalisation of the WHT and the even-length DFT. The matrix representing a primary GRJT is permutation-equivalent to the DFT matrix of even order, and in addition possesses the property to have a border consisting entirely of ??1's. To the authors ' knowledge, the problem of existence...
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