A Linear Algebra Problem Over Finite Fields.

摘要

Let K = GF(q) denote the finite field of order q, let G denote the group of one-to-one maps (permutations) of K onto K, and let GL(n,K) denote the group of n x n invertible matrices over K. Each triple (alpha(1), alpha(2),A) elements of GxGxGL(n,K) determines a permutation of the vector space K super n, of n x 1 matrices over K as follows: Pi(X) = alpha(1) inverse A alpha(2)(X); X element of K super n, where alpha(1), acts on X component-wise and A acts on x via matrix multiplication. Two triples alpha(1), alpha(2),A) and (beta(1), beta(2),B) are called equivalent if they determine the same permutation II. This paper determines for given ( alpha(1), alpha(2), A) those equivalent (beta(1), beta(2), B).