@article{369f72d5bede497fb57f7e88ec7790fa,

title = "Solving linear equations in a vector space over a finite field",

abstract = "We study the maximum possible size of a subset in a vector space over a finite field which contains no solution of a given linear equation (or a system of linear equations). This is a finite field version of Ruzsa's work [7].",

keywords = "Additive combinatorics, Arithmetic progression, Finite field model, Sidon set",

author = "Masato Mimura and Norihide Tokushige",

note = "Funding Information: The authors thank the referees for their very careful reading and many helpful suggestions including the improvement of the exponents of the bounds in Theorem 14 (from 5/8 to 1/2) and Theorem 15 (from 7/8 to 3/4). Masato Mimura is supported in part by JSPS KAKENHI Grant Number JP17H04822 , and Norihide Tokushige is supported by JSPS KAKENHI Grant Number JP18K03399 . Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = dec,

doi = "10.1016/j.disc.2021.112603",

language = "English",

volume = "344",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "12",

}