## Abstract

For a k-subset X of Zn, the set of differences on X is the set ΔX={i-j (mod n): i,jεX,i≠j}. A conflict-avoiding code CAC of length n and weight k is a collection C of k-subsets of Zn such that ΔXΔY = ø for any distinct X,YεC. Let CAC(n,k) be the class of all the CACs of length n and weight k. The maximum size of codes in CAC(n, k) is denoted by M(n,k). A code Cε CAC(n, k) is said to be optimal if |C| = M(n,k). An optimal code C is tight equi-difference if |CΔX = Zn\{0} and each codeword in C is of the form {0,i,2i,⋯,(k-1)i}. In this paper, the necessary and sufficient conditions for the existence problem of optimal tight equi-difference conflict-avoiding codes of length n = 2k±1 and weight 3 are given.

Original language | English |
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Pages (from-to) | 223-231 |

Number of pages | 9 |

Journal | Journal of Combinatorial Designs |

Volume | 21 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2013 |

## Keywords

- conflict-avoiding codes
- equi-difference
- optimal codes

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