Extension theorems for Hamming varieties over finite fields

Daewoong Cheong, Doowon Koh, Thang Pham

We study the finite field extension estimates for Hamming varieties $H_j,j\in {\mathbb{F}}_q^{\ast },$ defined by $H_j=\{x\in {\mathbb{F}}_q^d:{\prod }_{k=1}^d{x}_k=j\},$ where ${\mathbb{F}}_q^d$ d…