# Bivectors over a Finite Field

MacDougall, James A. (1981) Bivectors over a Finite Field. Canadian Mathematical Bulletin, 24 . pp. 489-490.

 Preview
PDF - Accepted Version
Let $U$ be an $n$-dimensional vector space over a finite field of $q$ elements. The number of elements of $A^2 U$ of each irreduaile length is found using the isomorphism of $A^2 U$ with $H_n$ the space of $n \times n$ skew-symmetric matrices, and results due to Carlitz and MacWilliams on the number of skew-symmetric matrices of any given rank.