论文标题
缩短了APN和PN函数的线性代码
Shortened linear codes from APN and PN functions
论文作者
论文摘要
由完美非线性（PN）和几乎完美的非线性（APN）函数和一阶Reed-Muller代码的组件函数生成的线性代码一直是编码理论中深入研究的对象。本文的目的是研究来自APN函数的两个线性代码系列的一些二元缩短代码，以及与PN函数相关的一些$ p $ yar的缩短代码。这些缩短的代码的重量分布及其双重参数是确定的。这些二进制代码和$ P $ ARY代码的参数是灵活的。本文介绍的许多代码都是最佳或几乎最佳的。本文的结果表明，缩短技术对于构建良好的代码非常有前途。
Linear codes generated by component functions of perfect nonlinear (PN) and almost perfect nonlinear (APN) functions and the first-order Reed-Muller codes have been an object of intensive study in coding theory. The objective of this paper is to investigate some binary shortened codes of two families of linear codes from APN functions and some $p$-ary shortened codes associated with PN functions. The weight distributions of these shortened codes and the parameters of their duals are determined. The parameters of these binary codes and $p$-ary codes are flexible. Many of the codes presented in this paper are optimal or almost optimal. The results of this paper show that the shortening technique is very promising for constructing good codes.
