Improved Error Bounds for the Distance Distribution of Reed-Solomon Codes
Zhicheng Gao, Jiyou Li · IEEE Transactions on Information Theory · 2023
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.