Geodesic
Bivectors over a Finite Field
Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 489-490

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DOI

Let U be an n -dimensional vector space over a finite field of q elements. The number of elements of Λ2U of each irreducible length is found using the isomorphism of Λ2U with Hn, the space of n x n skew-symmetric matrices, and results due to Carlitz and MacWilliams on the number of skew-symmetric matrices of any given rank.
DOI : 10.4153/CMB-1981-073-8
Mots-clés : 15A75, Grassmann Spaces, Exterior powers 
MacDougall, J. A. Bivectors over a Finite Field. Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 489-490. doi: 10.4153/CMB-1981-073-8
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     title = {Bivectors over a {Finite} {Field}},
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     year = {1981},
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     doi = {10.4153/CMB-1981-073-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-073-8/}
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