Based on the construction of a new distance-preserving Gray map from（（Fp + uFp）N, Gray distance） to(the corresponding Gray images in FppN, Hamming distance) and the calculation of Gray distances of（u-1）-constacyclic codes over Fp + uFp, a bound for the Hamming distances of a class of negacyclic codes with length p N over Fp is obtained, which is more tighter than Singleton bound. Further more, the exact Hamming distances of some p-ary negacyclic codes are determined from this bound, some of which cannot be got from Dinh’s work published on Finite Fields and Their Applications in 2008.
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