2022/05/04 by Gao, Zhicheng, Li, Jiyou
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2205.02277
We use the generating function approach to derive simple expressions for the factorial moments of the distance distribution over Reed-Solomon codes. We obtain better upper bounds for the error term of a counting formula given by Li and Wan, which gives nontrivial estimates on the number of polynomials over finite fields with prescribed leading coefficients and a given number of linear factors. This improvement leads to new results on the classification of deep holes of Reed Solomon codes.