Flash Memories
Towards 3-query locally decodable codes of subexponential length
Journal of the ACM (JACM)
3-query locally decodable codes of subexponential length
Proceedings of the forty-first annual ACM symposium on Theory of computing
Correcting limited-magnitude errors in the rank-modulation scheme
IEEE Transactions on Information Theory
Permutation arrays under the Chebyshev distance
IEEE Transactions on Information Theory
Distance-preserving mappings from binary vectors to permutations
IEEE Transactions on Information Theory
| Hi-index | 754.84 |
A frequency permutation array (FPA) of length n = mλ and distance d is a set of permutations on a multiset over m 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 Chebyshev distance, we first prove lower and upper bounds on the size of FPA. Then we give several constructions of FPAs, and some of them come with efficient encoding and decoding capabilities. Moreover, we show one of our designs is locally decodable, i.e., we can decode a message bit by reading at most λ + 1 symbols, which has an interesting application to private information retrieval.