## Abstract

We give a new construction of the extended binary Golay code. The construction is carried out by taking the Gray image of a self-dual linear code over the ring R = F+_{2} + uF_{2} + vF_{2} + uvF_{2} of length 6 and size 2^{12}.Writing a typical generating matrix of the form [I_{3}|A], with A being a 3×3 matrix over R, and finding some dependencies among the entries of A, we are able to set a general form for the generating matrices of self-dual codes of length 6. Using some special properties of elements of R, we end up with a family of generating matrices all of which give us the extended binary Golay code. We also prove the minimum distance property analytically.

Original language | English (US) |
---|---|

Pages (from-to) | 69-72 |

Number of pages | 4 |

Journal | Applied Mathematics and Information Sciences |

Volume | 8 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2014 |

Externally published | Yes |

## Keywords

- Codes over rings
- Extended binary Golay code
- Extremal codes
- Gray map
- Lee weight
- Self-dual codes

## ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics