Geodesic
Pairs of Bilinear Equations in a Finite Field
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 561-565

Voir la notice de l'article provenant de la source Cambridge University Press

Let F = GF(g) be the finite field of q = pr elements, p arbitrary. We wish to consider the system of bilinear equations 1.1 where all coefficients are from F. The number of solutions in F of a single bilinear equation may be obtained from a theorem of John H. Hodges (3, Theorem 3) by properly defining the matrices U, V, A, B. In 1954, L. Carlitz (1) obtained, as a special case of his work on quadratic forms, the number of simultaneous solutions in F of (1.1) when all aj = 1 and p is odd. Carlitz considered the case p = 2 separately. 
Porter, A. Duane. Pairs of Bilinear Equations in a Finite Field. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 561-565. doi: 10.4153/CJM-1966-054-9
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[1] 1. Carlitz, L., Pairs of quadratic equations in a finite field., Amer. J. Math., 76 (1954), 137–153. Google Scholar

[2] 2. Cohen, E., Simultaneous pairs cf linear and quadratic equations in a Galois field, Can. J. Math., 9 (1957), 74–78. Google Scholar

[3] 3. Hodges, J. H., Representations by bilinear forms in a finite field, Duke Math. J., 22 (1955), 497–509. Google Scholar

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