## Abstract

Given v, t, and m, does there exist a partial Steiner triple system of order v with t triples whose triples can be ordered so that any m consecutive triples are pairwise disjoint? Given v, t, and m _{1},m _{2},.. ,m _{s} with t = Σ _{i=1} ^{s} m _{i}, does there exist a partial Steiner triple system with t triples whose triples can be partitioned into partial parallel classes of sizes m _{1},.. ,m _{s}? An affirmative answer to the first question gives an affirmative answer to the second when m _{i} ≥ m for each i ε {1, 2,.. ., s}. These questions arise in the analysis of erasure codes for disk arrays and that of codes for unipolar communication, respectively. A complete solution for the first problem is given when m is at most 1/3 (v - (9v) ^{2/3})+O(v ^{1/3}).

Original language | English (US) |
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Pages (from-to) | 199-212 |

Number of pages | 14 |

Journal | Designs, Codes, and Cryptography |

Volume | 65 |

Issue number | 3 |

DOIs | |

State | Published - Dec 2012 |

## Keywords

- Kirkman signal set
- Kirkman triple system Hanani triple system
- Resolvable triple system
- Steiner triple system

## ASJC Scopus subject areas

- Computer Science Applications
- Applied Mathematics