Combinatorial Properties of Codes With $w$-Identifiable Parents Property

Abstract

In this paper, we study the combinatorial properties of $w$-IPP (identifiable parents property) codes and give necessary and sufficient conditions for a code to be a $w$-IPP code. Furthermore, let $R(C)=\frac{1}{n}{\log }_q|C|$ denote the rate of the $q$-ary code $C$ of length $n$, suppose $q\ge 3$ is a prime power, we prove that there exists a sequence of linear $q$-ary $2$-IPP codes $C_n$ of length $n$ with $R(C_n)=\frac{1}{3}log\frac{q^3}{4q^2-6q+3}$.