Words of minimal weight and weight distribution of binary Goppa codes

Little is known about the weight distribution of binary Goppa codes, however it is sure that it is close to a binomial distribution [F. Levy-dit-Vehel, et al., 1997]. That is, the number of words of weight w in a code of length n is approximately (_n^w)×2^k-n. This is true when w is not too small, but when w is close to 0 the distribution is not the same: for instance, for any weight from 1 to 2t the number of words is 0. Using an algorithm to find words of minimal weight we were able to perform some statistics on the small weights distribution and show that even for weights close to the minimal weight bound, the distribution is still binomial-like.