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On the Distribution of Weights Less Than 2wminin Polar Codes | IEEE Journals & Magazine | IEEE Xplore
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On the Distribution of Weights Less Than 2wminin Polar Codes


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 More

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)
Page(s): 5988 - 6000
Date of Publication: 07 May 2024

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