Additive bases of vector spaces over prime fields
Journal of Combinatorial Theory Series A
On the classification of geometric codes by polynomial functions
Designs, Codes and Cryptography
Handbook of Coding Theory
The permanent of a square matrix
European Journal of Combinatorics
The factorization of the permanent of a matrix with minimal rank in prime characteristic
Designs, Codes and Cryptography
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There is polynomial function X q in the entries of an m 脳 m(q 驴 1) matrix over a field of prime characteristic p, where q = p h is a power of p, that has very similar properties to the determinant of a square matrix. It is invariant under multiplication on the left by a non-singular matrix, and under permutations of the columns. This gives a way to extend the invariant theory of sets of points in projective spaces of prime characteristic, to make visible hidden structure. There are connections with coding theory, permanents, and additive bases of vector spaces.