Hamming Distances in Vector Spaces over Finite Fields

10/12/2019

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by   Esen Aksoy Yazici, et al.

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Let F_q be the finite field of order q and E⊂F_q^d, where 4|d. Using Fourier analytic techniques, we prove that if |E|>q^d-1/ddd/2d/2d/4, then the points of E determine a Hamming distance r for every even r.