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 Π, forming a Baer subline in the quotient space of Π. 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 [4], and C2(X), X a non-singular Hermitian variety [5]. Dedicated to the memory of András Gács (1969-2009)