de Mathématiques de Luminy
On the small weight codewords of the functional codes C2(Q), Q a non-singular quadric
We study the small weight codewords of the functional code C2(Q), with Q non-singular quadric of PG(N, q). We prove that the small weight codewords correspond to the intersections of Q with the singular quadrics of PG(N, q) consisting of two hyperplanes. We also calculate the number of codewords having these small weights.