### Abstract

A family of n-dimensional unit norm vectors is an Euclidean superimposed code if the sums of any two distinct at most m-tuples of vectors are separated by a certain minimum Euclidean distance d. Ericson and Györfl [8] proved that the rate of such a code is between (log m)/4m and (log m)/m for m large enough. In this paper-improving the above long-standing best upper bound for the rate-it is shown that the rate is always at most (logm)/2m, i.e., the size of a possible superimposed code is at most the root of the size given in [8]. We also generalize these codes to other normed vector spaces.

Original language | English |
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Pages (from-to) | 799-802 |

Number of pages | 4 |

Journal | IEEE Transactions on Information Theory |

Volume | 45 |

Issue number | 2 |

DOIs | |

Publication status | Published - Dec 1 1999 |

### Keywords

- Codes
- Growth rate
- Superimposed geometric codes

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

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## Cite this

Füredi, Z., & Ruszinkó, M. (1999). An improved upper bound of the rate of euclidean superimposed codes.

*IEEE Transactions on Information Theory*,*45*(2), 799-802. https://doi.org/10.1109/18.749032