## Abstract

For a set C of words of length 4 over an alphabet of size n, and for a, b ∈ C, let D(a, b) be the set of all descendants of a and b, that is, all words x of length 4 where x_{i} ∈ {a_{i}, b_{i}} for all 1 ≤ i ≤ 4. The code C satisfies the Identifiable Parent Property if for any descendant of two code-words one can identify at least one parent. The study of such codes is motivated by questions about schemes that protect against piracy of software. Here we show that for any ε > 0, if the alphabet size is n > n_{0}(ε) then the maximum possible cardinality of such a code is less than εn^{2} and yet it is bigger than n^{2-ε}. This answers a question of Hollmann, van Lint, Linnartz, and Tolhuizen. The proofs combine graph theoretic tools with techniques in additive number theory.

Original language | English (US) |
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Pages (from-to) | 349-359 |

Number of pages | 11 |

Journal | Journal of Combinatorial Theory. Series A |

Volume | 95 |

Issue number | 2 |

DOIs | |

State | Published - Aug 2001 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics