### Abstract

A frequency permutation array (FPA) of length n = mλ and distance d is a set of permutations on a multiset over rri symbols, where each symbol appears exactly λ times and the distance between any two elements in the array is at least d. FPA generalizes the notion of permutation array. In this paper, under the distance metric l∞-norm, we first prove lower and upper bounds on the size of FPA. Then we give a construction of FPA with efficient encoding and decoding capabilities. Moreover, we show our design is locally decodable, i.e., we can decode a message bit by reading at most λ+ 1 symbols, which has an interesting application for private information retrieval.

Original language | English |
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Title of host publication | 2009 IEEE International Symposium on Information Theory, ISIT 2009 |

Pages | 2713-2717 |

Number of pages | 5 |

DOIs | |

State | Published - 19 Nov 2009 |

Event | 2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of Duration: 28 Jun 2009 → 3 Jul 2009 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8102 |

### Conference

Conference | 2009 IEEE International Symposium on Information Theory, ISIT 2009 |
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Country | Korea, Republic of |

City | Seoul |

Period | 28/06/09 → 3/07/09 |

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## Cite this

*2009 IEEE International Symposium on Information Theory, ISIT 2009*(pp. 2713-2717). [5205867] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2009.5205867