Words of Minimal Weight and Weight Distribution in Binary Goppa Codes

The weight distribution of a Goppa code is proven to be “close” to the binomial weight distribution found in a random linear code. Some bounds have been found on the distance between the two distributions and this distance is incredibly small for some particular weights. However, for smaller weights the bound on the distance is of no use. Using an algorithm to find words of minimal weight we were able to perform some statistics on these weight distributions and show that even for weights close to the minimal weight bound the distribution is still binomial-like.