An Upper and a Lower Bound on the Probability of an Undetected Error for Binary Expansions of Generalized Reed-Solomon Codes

Abstract

By utilizing certain characteristic structure of the Hamming weight distribution of maximum distance separable codes, we can get weight enumerators to compute an upper and a lower bound on the probability of an undetected error for binary expansions of generalized Reed-Solomon (GRS) codes. Also, values of the average probability of an undetected error are computed by using the average binary weight distribution for an ensemble of binary expansions of all GRS codes for some given concrete code parameters. By comparing these values with values of the upper and the lower bound computed by using the proposed weight enumerators, the effectiveness of those weight enumerators is shown in this paper.