Hamming Distances in Vector Spaces over Finite Fields

2019/10/12 by Esen Aksoy Yazici, Yazici, Esen Aksoy · 1 citation
Mathematics · #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1910.05557

openalex publication_date 2019/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• A note on the distinct distances problem over finite fields

Related

• Erdos distance problem in vector spaces over finite fields
• Hamming distances from a function to all codewords of a Generalized\n Reed-Muller code of order one
• On the two-parameter Erdős-Falconer distance problem over finite fields
• Pinned distance sets, Wolff's exponent in finite fields and improved sum-product estimates
• The Erdös-Falconer distance problem on the unit sphere in vector spaces over finite fields