Weight distribution of Hermitian codes and matrices rank

We are interested in calculating the weight distribution of Hermitian codes over the finite field with q2 elements. In this work we show that, if we can compute the partial weight distribution for about q2 weights, then we will easily compute the whole weight distribution (which has about q3 values). To achieve this, we actually show that the computation of a given element of the weight distribution is equivalent to a less laborious task, which is the classification of some submatrices of the parity-check matrix according to their rank.