Geodesic
On C-Matrices of Arbitrary Powers
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 531-535

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

A C-matrix is a square matrix of order m + 1 which is 0 on the main diagonal, has ±1 entries elsewhere and satisfies . Thus, if , I + C is an Hadamard matrix of skew type [3; 6] and, if , iI + C is a (symmetric) complex Hadamard matrix [4]. For m > 1, we must have . Such matrices arise from the quadratic character χ in a finite field, when m is an odd prime power, as [χ(ai – aj )] suitably bordered, and also from some other constructions, in particular those of skew type Hadamard matrices. (For we must have m = a 2 + b 2, a, b integers.) 
Turyn, Richard J. On C-Matrices of Arbitrary Powers. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 531-535. doi: 10.4153/CJM-1971-056-0
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