Decoding frequency permutation arrays under infinite norm
Min-Zheng Shieh, Shi‐Chun Tsai · 2009
A frequency permutation array (FPA) of length n = m¿ and distance d is a set of permutations on a multiset over m symbols, where each symbol appears exactly ¿ 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 ¿¿-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 ¿ + 1 symbols, which has an interesting application for private information retrieval.