[Resource Topic] 2007/276: Prolific Codes with the Identifiable Parent Property

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Prolific Codes with the Identifiable Parent Property

Authors: Simon R. Blackburn, Tuvi Etzion, Siaw-Lynn Ng


Let C be a code of length n over an alphabet of size q. A word d is a descendant of a pair of codewords x,y if d_i lies in {x_i ,y_i } for 1 <= i <= n. A code C is an identifiable parent property (IPP) code if the following property holds. Whenever we are given C and a descendant d of a pair of codewords in C, it is possible to determine at least one of these codewords. The paper introduces the notion of a prolific IPP code. An IPP code is prolific if all q^n words are descendants. It is shown that linear prolific IPP codes fall into three infinite (`trivial’) families, together with a single sporadic example which is ternary of length 4. There are no known examples of prolific IPP codes which are not equivalent to a linear example: the paper shows that for most parameters there are no prolific IPP codes, leaving a relatively small number of parameters unsolved. In the process the paper obtains upper bounds on the size of a (not necessarily prolific) IPP code which are better than previously known bounds.

ePrint: https://eprint.iacr.org/2007/276

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