摘要
A code is said to be a w-identifiable parent property code (or w-IPP code for short) if whenever d is a descendant of w (or fewer) codewords, and one can always identify at least one of the parents of d. Let C be an (N,w + 1,q)-code and C* an (w + 1)-color graph for C. If a graph G is a subgraph of C* and consists of w +1 edges with different colors, then G is called a (w +1)-pattern of C*. In this paper, we proved that C is a w-IPP code if and only if there exists at most one vertex with color degree more than 1 in any (w + 1)-pattern of C*.
A code is said to be a w-identifiable parent property code （or w-IPP code for short） if whenever d is a descendant of w （or fewer） codewords, and one can always identify at least one of the parents of d. Let C be an （N, w ＋ 1, q）-code and C＊ an （w ＋ 1）-color graph for C. If a graph G is a subgraph of C＊ and consists of w ＋ 1 edges with different colors, then G is called a （w ＋ 1）-pattern of C＊. In this paper, we proved that C is a w-IPP code if and only if there exists at most one vertex with color degree more than 1 in any （w ＋ 1）-pattern of C＊.
基金
the National Natural Science Foundation of China (No. 10471093)
