Abstract:
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) co...Show MoreMetadata
Abstract:
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 2w_{\min } , where w_{\min } 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 2w_{\min } . Moreover, the proposed enumeration algorithm runs in polynomial time with respect to the code length.
Published in: IEEE Transactions on Communications ( Volume: 72, Issue: 10, October 2024)