## Abstract

This paper studies codes C over GF(4) which have even weights and have the same weight distribution as the dual code C^{⊥}. Some of the results are as follows. All such codes satisfy C^{⊥} = C (If C^{⊥}= C, T has a binary basis.) The number of such C's is determined, and those of length ≤14 are completely classified. The weight enumerator of C is characterized and an upper bound obtained on the minimum distance. Necessary and sufficient conditions are given for C to be extended cyclic. Two new 5-designs are constructed. A generator matrix for C can be taken to have the form [I | B], where B^{⊥} = B. We enumerate and classify all circulant matrices B with this property. A number of open problems are listed.

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

Pages (from-to) | 288-318 |

Number of pages | 31 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 25 |

Issue number | 3 |

DOIs | |

State | Published - Nov 1978 |