Determination of partial weight enumerators of BCH codes by Hash methods

The PWE (Partial Weight Enumerator) algorithm permits to obtain a partial weights enumerator for linear codes. This algorithm is based on the Multiple Impulse Method combined with a Monte Carlo Method. The main disadvantage of this algorithm is the height run time complexity when the set of selected codewords as sample is large. However, when this set is reduced it becomes not representative and the quality of approximation decrease. In this paper, we will present an improved version PWEH of the PWE algorithm based on Hash techniques in order to remedy this disadvantage. The comparison between PWE and PWEH shows that the run time of this latest is reduced at more than 5100%. PWEH is validated and it is used to find an approximation of the partial weight enumerators of BCH (255,199) code where the weight distributions is still unknown.