# even code

A binary code is called *even* if the Hamming weight of all its
codewords is even. Furthermore, a binary code is called
*doubly-even* if the Hamming weight of all its codewords is
divisible by $4$. An even code which is not doubly-even is said to be
*strictly even*.

Examples of doubly-even codes are the extended binary Hamming code of block length $8$ and the extended binary Golay code of block length $24$. These two codes are, in addition, self-dual.

Title | even code |
---|---|

Canonical name | EvenCode |

Date of creation | 2013-03-22 15:15:42 |

Last modified on | 2013-03-22 15:15:42 |

Owner | GrafZahl (9234) |

Last modified by | GrafZahl (9234) |

Numerical id | 4 |

Author | GrafZahl (9234) |

Entry type | Definition |

Classification | msc 94B05 |

Related topic | LinearCode |

Defines | doubly-even code |

Defines | strictly even code |