## Abstract

We give a new upper bound on the maximum size A_{q} (n, d) of a code of word length n and minimum Hamming distance at least d over the alphabet of q ≥ 3 letters. By block-diagonalizing the Terwilliger algebra of the nonbinary Hamming scheme, the bound can be calculated in time polynomial in n using semidefinite programming. For q = 3, 4, 5 this gives several improved upper bounds for concrete values of n and d. This work builds upon previous results of Schrijver [A. Schrijver, New code upper bounds from the Terwilliger algebra and semidefinite programming, IEEE Trans. Inform. Theory 51 (2005) 2859-2866] on the Terwilliger algebra of the binary Hamming scheme.

Original language | English |
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Pages (from-to) | 1719-1731 |

Number of pages | 13 |

Journal | Journal of Combinatorial Theory. Series A |

Volume | 113 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2006 Nov |

## Keywords

- Block-diagonalization
- Codes
- Delsarte bound
- Nonbinary codes
- Semidefinite programming
- Terwilliger algebra
- Upper bounds

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics