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A frequency permutation array (FPA) of length $n=m\lambda$ and distance $d$is a set of permutations on a multiset over $m$ symbols, where each symbolappears exactly $\lambda$ times and the distance between any two elements inthe array is at least $d$. FPA generalizes the notion of permutation array. Inthis paper, under the distance metric $\ell_\infty$-norm, we first prove lowerand upper bounds on the size of FPA. Then we give a construction of FPA withefficient encoding and decoding capabilities. Moreover, we show our design islocally decodable, i.e., we can decode a message bit by reading at most$\lambda+1$ symbols, which has an interesting application for privateinformation retrieval.

Decoding Frequency Permutation Arrays under Infinite norm