2023/08/19 by Ye, Zicheng, Li, Yuan, Zhang, Huazi +3
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2308.10024
The number of low-weight codewords is critical to the performance of error-correcting codes. In 1970, Kasami and Tokura characterized the codewords of Reed-Muller (RM) codes whose weights are less than 2wmin, where wmin represents the minimum weight. In this paper, we extend their results to decreasing polar codes. We present the closed-form expressions for the number of codewords in decreasing polar codes with weights less than 2wmin. Moreover, the proposed enumeration algorithm runs in polynomial time with respect to the code length.