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Distance-increasing mappings from binary vectors to permutations that increase hamming distances by at least two

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1 Author(s)
Jen-Chun Chang ; Dept. of Comput. Sci. & Inf. Eng., Nat. Taipei Univ., Taipei County

In this correspondence, for any k ges 2, we first propose two constructions of (n,k) distance-increasing mappings (DIMs) from the set of binary vectors of length n to the set of permutations of the same length that strictly increase the Hamming distance by at least k except when it is obviously not possible. Next, we prove that for any k ges 2, there is a smallest positive integer nk such that an (n,k) DIM can be constructed for any n ges nk. An explicit upper bound on nk is also given

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Information Theory, IEEE Transactions on  (Volume:52 ,  Issue: 4 )