Cyclic Group Projection for Enumerating Quasi-Cyclic Codes Trapping Sets

Vasiliy Usatyuk; Yury Kuznetsov; Sergey Egorov

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arXiv · 2401.14810

Cyclic Group Projection for Enumerating Quasi-Cyclic Codes Trapping Sets

Vasiliy Usatyuk·Yury Kuznetsov·Sergey Egorov

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Abstract

This paper introduces a novel approach to enumerate and assess Trapping sets in quasi-cyclic codes, those with circulant sizes that are non-prime numbers. Leveraging the quasi-cyclic properties, the method employs a tabular technique to streamline the importance sampling step for estimating the pseudo-codeword weight of Trapping sets. The presented methodology draws on the mathematical framework established in the provided theorem, which elucidates the behavior of projection and lifting transformations on pseudo-codewords

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Vasiliy Usatyuk, Yury Kuznetsov, Sergey Egorov. 2024-01-26. Cyclic Group Projection for Enumerating Quasi-Cyclic Codes Trapping Sets. https://arxiv.org/abs/2401.14810

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