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

## TL;DR

This paper establishes a relationship between the weight distribution of concatenated code ensembles using the Plotkin construction and their component codes, aiding in analyzing complex code structures like Reed-Muller-like codes.

## Contribution

It introduces a novel relation linking the weight distributions of concatenated codes and their components, facilitating easier analysis of complex code ensembles.

## Key findings

- Derived a relation between weight distributions of concatenated and component codes
- Applicable to Reed-Muller-like codes and other code ensembles
- Simplifies the calculation of ensemble weight distributions

## 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.