### 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) |
---|---|

Pages (from-to) | 199-212 |

Number of pages | 14 |

Journal | Designs, Codes, and Cryptography |

Volume | 65 |

Issue number | 3 |

DOIs | |

State | Published - Dec 2012 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computer Science Applications

### Cite this

*Designs, Codes, and Cryptography*,

*65*(3), 199-212. https://doi.org/10.1007/s10623-011-9521-1

**Trails of triples in partial triple systems.** / Colbourn, Charles; Horsley, Daniel; Wang, Chengmin.

Research output: Contribution to journal › Article

*Designs, Codes, and Cryptography*, vol. 65, no. 3, pp. 199-212. https://doi.org/10.1007/s10623-011-9521-1

}

TY - JOUR

T1 - Trails of triples in partial triple systems

AU - Colbourn, Charles

AU - Horsley, Daniel

AU - Wang, Chengmin

PY - 2012/12

Y1 - 2012/12

N2 - 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).

AB - 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).

KW - Kirkman signal set

KW - Kirkman triple system Hanani triple system

KW - Resolvable triple system

KW - Steiner triple system

UR - http://www.scopus.com/inward/record.url?scp=84868361050&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868361050&partnerID=8YFLogxK

U2 - 10.1007/s10623-011-9521-1

DO - 10.1007/s10623-011-9521-1

M3 - Article

AN - SCOPUS:84868361050

VL - 65

SP - 199

EP - 212

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

SN - 0925-1022

IS - 3

ER -