The small weight codewords of the functional codes associated to non-singular Hermitian varieties

This article studies the small weight codewords of the functional code CHerm(X), with X a non-singular Hermitian variety of PG(N, q2). The main result of this article is that the small weight codewords correspond to the intersections of X with the singular Hermitian varieties of PG(N, q2) consisting of q + 1 hyperplanes through a common (N -2)-dimensional space , forming a Baer subline in the quotient space of . The number of codewords having these small weights is also calculated. In this way, similar results are obtained to the functional codes C2(Q), Q a non-singular quadric [?], and C2(X), X a non-singular Hermitian variety [?]. Dedicated to the memory of Andr

• Type: Journal
• Year: 2010
• Where: DCC
• Authors: Frédéric A. B. Edoukou, Anja Hallez, François Rodier, Leo Storme
• Keywords: Computer Graphics, DCC 2010, Non-singular Hermitian Variety, Small Weight Codewords, Small Weights