On the small weight codewords of the functional codes C_2(Q), Q a non-singular quadric

Frédéric Edoukou (1) , Anja Hallez (2) , François Rodier (1) , Leo Storme (2)

1 IML - Institut de mathématiques de Luminy
2 Department of pure mathematics and computer algebra [Gent]

We study the small weight codewords of the functional code C_2(Q), with Q a 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.

Domaines: Géométrie algébrique [math.AG]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Frédéric Edoukou, Anja Hallez, François Rodier, Leo Storme. On the small weight codewords of the functional codes C_2(Q), Q a non-singular quadric. 2009. ⟨hal-00356568⟩