On the Distribution of Weights Less than 2wmin in Polar Codes

Apr 19, 2026

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Low-weight codewords determine the error-correcting performance of linear codes, motivating exact enumeration of codewords below a weight threshold. This work extends Kasami and Tokura’s characterization of Reed–Muller codes to decreasing polar codes. Closed-form expressions are derived for the number of codewords in decreasing polar codes with weights less than 2wmin. An enumeration algorithm is provided with polynomial-time complexity in the code length.

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On the Distribution of Weights Less than 2wmin in Polar Codes

Apr 19, 2026

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