A Method to determine Partial Weight Enumerator for Linear Block Codes

Abstract

In this paper we present a fast and efficient method to find partial weight enumerator (PWE) for binary linear block codes by using the error impulse technique and Monte Carlo method.  This PWE can be used to compute an upper bound of the error probability for the soft decision maximum likelihood decoder (MLD). As application of this method we give partial weight enumerators and analytical performances of the BCH(130,66) , BCH(103,47) and BCH(111,55) shortened codes; the first code is obtained by shortening the binary primitive BCH (255,191,17) code and the two other codes are obtained by shortening the binary primitive BCH(127,71,19) code. The weight distributions of these three codes are unknown at our knowledge.

Keywords: Error impulse technique, partial weight enumerator, maximum likelihood performance, error correcting codes, shortened BCH codes, Monte Carlo method.