Codes and projective multisets.
Optimal four-dimensional codes over .
Remarks on a paper of Tallini
The minimum size of complete caps in .
The weight distribution of the functional codes defined by forms of degree 2 on Hermitian surfaces
We study the functional codes defined on a projective algebraic variety , in the case where is a non-degenerate Hermitian surface. We first give some bounds for , which are better than the ones known. We compute the number of codewords reaching the second weight. We also estimate the third weight, show the geometrical structure of the codewords reaching this third weight and compute their number. The paper ends with a conjecture on the fourth weight and the fifth weight of the code .