2024/02/20 by Mohammad Rowshan, Rowshan, Mohammad, Vlad Drăgoi +3 · 1 citation
Computer Science · Engineering · #Advanced Data Storage Technologies #Advanced Wireless Communication Techniques #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2402.12707
openalex publication_date 2024/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The structure of a linear block code is pivotal in defining fundamental properties, particularly weight distribution, and code design. In this study, we characterize the Type II structure of polar codewords with weights less than twice the minimum weight wmin, utilizing the lower triangular affine (LTA) transform. We present a closed-form formula for their enumeration. Leveraging this structure and additionally characterizing the structure of weight 2wmin, we ascertain the complete weight distribution of low-rate and, through the utilization of dual codes properties, high-rate polar codes, subcodes of Reed--Muller (RM) codes, and RMxPolar codes. Furthermore, we introduce a partial order based on the weight distribution and briefly explore its properties and applications in code construction and analysis.