### Abstract

Let M(n, A) denote the maximum possible cardinality of a family of binary strings of length n, such that for every four distinct members of the family there is a coordinate in which exactly two of them have a 1. We prove that M(n,A) ≤ 2^{0.78n} for all sufficiently large n. Let M(n, C) denote the maximum possible cardinality of a family of binary strings of length n, such that for every four distinct members of the family there is a coordinate in which exactly one of them has a 1. We show that there is an absolute constant c < 1/2 such that M(n, C) ≤ 2^{cn} for all sufficiently large n. Some related questions are discussed as well.

Original language | English (US) |
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Pages (from-to) | 381-390 |

Number of pages | 10 |

Journal | Combinatorics Probability and Computing |

Volume | 9 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 2000 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

Alon, N., Körner, J., & Monti, A. (2000). String Quartets in Binary.

*Combinatorics Probability and Computing*,*9*(5), 381-390. https://doi.org/10.1017/S0963548300004375