## Abstract

The two 1-error correcting perfect binary codes, C and C^{′} are said to be equivalent if there exists a permutation π of the set of the n coordinate positions and a word over(d, ̄) such that C^{′} = π (over(d, ̄) + C). Hessler defined C and C^{′} to be linearly equivalent if there exists a non-singular linear map φ such that C^{′} = φ (C). Two perfect codes C and C^{′} of length n will be defined to be extended equivalent if there exists a non-singular linear map φ and a word over(d, ̄) such that C^{′} = φ (over(d, ̄) + C) . Heden and Hessler, associated with each linear equivalence class an invariant L_{C} and this invariant was shown to be a subspace of the kernel of some perfect code. It is shown here that, in the case of extended equivalence, the corresponding invariant will be the extension of the code L_{C}. This fact will be used to give, in some particular cases, a complete enumeration of all extended equivalence classes of perfect codes.

Original language | English |
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Pages (from-to) | 43-55 |

Number of pages | 13 |

Journal | Discrete Mathematics |

Volume | 310 |

Issue number | 1 |

DOIs | |

Publication status | Published - 6 Jan 2010 |

MoE publication type | A1 Journal article-refereed |

## Keywords

- Perfect codes
- Side class structures