Abstract
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*.
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Foundation item: the National Natural Science Foundation of China (No. 10471093)
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Ma, J., Xiong, Y. On codes with w-identifiable parent property. J. Shanghai Jiaotong Univ. (Sci.) 13, 487–490 (2008). https://doi.org/10.1007/s12204-008-0487-8
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DOI: https://doi.org/10.1007/s12204-008-0487-8