极化码的权重结构教程
A Tutorial on Weight Structure of Polar Codes
AI总结：
本教程介绍极化码权重结构的代数基础，基于单项式多项式形式将极化码与里德-穆勒码视为递减单项式码，阐述仿射自同构等内容，助力读者深入理解极化码权重分布相关技术文献。
AI中文摘要：
本教程介绍了极化码权重结构的代数基础。采用基于单项式的多项式形式体系，我们解释了如何将极化码和里德-穆勒码视为递减单项式码，从而实现对低重量码字的系统表征与枚举。其目标是提供对仿射自同构、基于轨道的最小及低重量码字描述，以及它们在权重枚举中的作用的易懂介绍。通过示例及递归和陪集技术的高级概述，本文旨在让读者为更深入地理解近期关于极化码权重分布的技术文献做好准备。
英文摘要：
This tutorial introduces the algebraic foundations underlying the weight structure of polar codes. Using a monomial-based polynomial formalism, we explain how polar and Reed-Muller codes can be viewed as decreasing monomial codes, enabling systematic characterization and enumeration of low-weight codewords. Its goal is to provide an accessible introduction to affine automorphisms, orbit-based descriptions of minimum and low-weight codewords, and their role in weight enumeration. Through illustrative examples and high-level overviews of recursive and coset-based techniques, the paper aims to prepare readers for deeper engagement with the recent technical literature on the weight distribution of polar codes.
