Cyclic Group Projection for Enumerating Quasi-Cyclic Codes Trapping Sets
This work addresses a specific challenge in coding theory for quasi-cyclic codes, but it appears incremental as it builds on existing mathematical frameworks without claiming broad breakthroughs.
The paper tackled the problem of enumerating and assessing Trapping sets in quasi-cyclic codes with non-prime circulant sizes by introducing a novel approach that leverages quasi-cyclic properties and a tabular technique to streamline importance sampling for estimating pseudo-codeword weight, resulting in a method that draws on a mathematical framework for projection and lifting transformations.
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