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On the p-rank of the incidence matrix of points and hyperplanes in a finite projective geometry

by: K. J. C. Smith
Journal of Combinatorial Theory, Vol. 7, No. 2. (September 1969), pp. 122-129, doi:10.1016/s0021-9800(69)80046-3  Key: citeulike:12010413

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Abstract

The rank over GF(p), or p-rank, of the incidence matrix of points and hyperplanes in the finite projective geometry PG(t, pn) is shown to be equal to This result is obtained by representing the points of the geometry by elements of the field K=GF(pn(t+1)) and by representing hyperplanes in terms of linear functionals on K expressed in terms of the trace from K to GF(pn).


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