# Introduction

This is a database of half-rate additive codes over GF(4). We have shown that all such codes (except a few degenerate cases) can be represented as directed graphs. For more details, see the paper [1].

^ TOP# Tables

Total number of (non-degenerate [1] and non-decomposable) half-rate additive codes over GF(4) of length n and minimum distance d:

d\n | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

1 | 1 | 4 | 27 | 322 | 8509 | 686,531 |

2 | 1 | 3 | 21 | 262 | 9653 | 1,279,641 |

3 | 1 | 9 | 644 | 253,635 | ||

4 | 1 | 3 | ||||

All | 2 | 7 | 49 | 593 | 18,807 | 2,219,810 |

Number of circulant and bordered circulant directed graph codes with highest minimum distance:

n | Max d | # Codes |
---|---|---|

2 | 2 | 1 |

3 | 2 | 2 |

4 | 3 | 1 |

5 | 3 | 3 |

6 | 4 | 1 |

7 | 4 | 2 |

8 | 4 | 11 |

9 | 4 | 22 |

10 | 5 | 4 |

11 | 5 | 21 |

12 | 6 | 2 |

13 | 6 | 2 |

14 | 6 | 54 |

15 | 6 | 325 |

16 | 7 | 1 |

17 | 7 | 9 |

18 | 8 | 1 |

19 | 7 | 1366 |

20 | 8 | 4 |

21 | 8 | 42 |

22 | 8 | 1328 |

23 | 8 | 8027 |

24 | 9 | 1 |

25 | 9 | 25 |

26 | 9 | 1877 |

# Files

Codes are stored as directed graphs. See the paper [1] for how to convert graphs to codes. Each line in the file is of the format "Graph [tab] Minimum distance". Graphs are stored on the format "#Vertices #Edges (List of directed edges)". For instance, the line "3 3 0 2 2 0 1 2 2" is a directed graph corresponding to a half-rate additive code over GF(4) of length 3 with minimum distance 2. The directed graph has 3 vertices and the 3 directed edges 0->2, 2->0, and 1->2.

All codes of length 2 to 7 are collected in one file.

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allcodes.txt |

All circulant and bordered circulant codes of length 2 to 26 with highest minimum distance are also collected in one file. (This file does not contain the minimum distance of codes, as these are given in the above table.)

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circulant.txt |

# References

[1] Lars Eirik Danielsen and Matthew G. Parker: Directed graph representation of half-rate additive codes over GF(4). Submitted for publication, Feb. 2009. (arXiv:0902.3883)