The Kronecker power corresponds to the polynomial ring first defined on a field , while the extension scheme corresponds to the extension field obtained as a quotient.
The elements of the Hadamard exponent matrix lie in the Galois field , and its row vectors constitute the codewords of what shall be called a generalized Hadamard code.
It is easy to construct a class of hash functions when D is field.
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For finite projective spaces of geometric dimension at least three, Wedderburn's little theorem implies that the division ring over which the projective space is defined must be a finite field, GF(q), whose order (that is, number of elements) is q (a prime power).
The block Wiedemann algorithm for computing kernel vectors of a matrix over a finite field is a generalisation of an algorithm due to Don Coppersmith.
University of Rome and in 1975 a Ph.D. from the University of Warwick under the supervision of George Lusztig (The mod-2 Cohomology of the orthogonal groups over a finite field).