This page is just for the electronic distribution for the unidirectional covering codes for the paper "Unidirectional Covering Codes". This table does not (necessarily) contain the current bounds for unidirectional covering codes, since no entries have been updated since the submission of the paper (Oct 2004).

Codewords are given by their decimal value (11 is ...01011), the files have the following format:

R ; First line - covering radius n ; Second line - length of the codewords q ; Third line - size of the alphabet K ; Fourth line - cardinality of the code ; K codewords in one or more lines

See the paper and its references for explanations and proofs for the
bounds on * E(n,R)*. Since the unidirectional
covering codes do not differ from (symmetric) covering codes for R=1,
these values are greyed. We did not improve any of these bounds and
they are listed here for the complicity.

n \ R | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

3 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

4 | 4 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

5 | 7 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

6 | 12 | 4 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

7 | 16 | o 8 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

8 | 32 | o 14 |
4 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 |

9 | 62 | e 21-24 |
t 8 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 |

10 | 107-120 | e 32-36 |
e 14-15 |
4 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 |

11 | 180-192 | e 53-68 |
e 21-26 |
t 8 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 |

12 | 342-380 | e 91-126 |
e 32-44 |
e 14-15 |
4 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 |

13 | 598-704 | e 157-240 |
e 48-74 |
e 20-26 |
t 8 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |

Lower bounds

Unmarked (R=1) | Lower bound on K(n,R) |

Unmarked (R>1) | Proposition 3.3, Corollary 3.2 |

o | IP_{exact} |

e | Exhaustive search |

t | Theorem 3.5 |

Upper bounds

Unmarked (R=1) | Upper bound on K(n,R) |

Unmarked (R>1) | Proposition 3.3, Corollary 3.2 |

Linked | Tabu search |