On the Weight Distribution of Concatenated Code Ensemble Based on the Plotkin Construction

2025/08/29 by Ma, Xiao
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2508.21515

Abstract

In this note, we reveal a relation between the weight distribution of a concatenated code ensemble based on the Plotkin construction and those of its component codes. The relation may find applications in the calculation of the ensemble weight distributions for many codes, including Reed-Muller (RM)-like codes.

Citations

• A Balanced Tree Approach to Construction of Length-Compatible Polar Codes
• Interleaved Polar (I-Polar) Codes
• Systematic Block Markov Superposition Transmission of Repetition Codes
• Block Markov Superposition Transmission: Construction of Big Convolutional Codes from Short Codes
• New Techniques for Upper-Bounding the ML Decoding Performance of Binary Linear Codes
• Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels

Related

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• On the weight distribution of convolutional codes
• Asymptotic Concentration Behaviors of Linear Combinations of Weight Distributions on Random Linear Code Ensemble
• MacWilliams Identities for Terminated Convolutional Codes
• Weight distributions of two classes of linear codes