gf-internal: Internal arithmetic helpers for GF(p), p prime

In PGM2: Recursive Construction of Nested Resolvable Designs and Associated Uniform Designs over GF(p)

Internal arithmetic helpers for GF(p), p prime

Description

Small utilities used by the design constructors: primality check and enumeration of the points of the projective geometry PG(m, p).

Details

Points of PG(m, p) are the nonzero vectors of GF(p)^(m+1) up to multiplication by a nonzero scalar. One canonical representative is kept per point (the one whose first nonzero coordinate equals 1), giving (p^(m+1) - 1)/(p - 1) points. Vectors are enumerated in base-p counting order with the first coordinate as the most significant digit, which for p = 2 reproduces exactly the point (and hence treatment) numbering of PGM2 <= 1.2.

PGM2 documentation built on Aug. 27, 2026, 9:07 a.m.