"A nonsingular cubic surface F can be rationally represented upon a plane α if and only if F contains a rational point."

“The study of the geometry of a Galois space Sr,q, i. e. of a projective r-dimensional space over a Galois field of order q = ph. where p, h are positive integers and p is a prime , has recently been pursued and developed along new lines ... In it, both algebraic-geometric and arithmetical methods have been applied, including the use of electronic calculating machines; moreover, some of the problems dealt with are deeply connected with information theory, especially with the construction of q-ary error-correcting codes. It is actually a chapter of arithmetical geometry, which reduces to the investigation of certain questions on congruences mod p in the particular case when h = 1.”