Sidon basis in polynomial rings over finite fields

Kuo, Wentang, and Yamagishi, Shuntaro. "Sidon basis in polynomial rings over finite fields." Czechoslovak Mathematical Journal 71.2 (2021): 555-562. <http://eudml.org/doc/298273>.

@article{Kuo2021,
abstract = {Let $\mathbb \{F\}_q[t]$ denote the polynomial ring over $\mathbb \{F\}_q$, the finite field of $q$ elements. Suppose the characteristic of $\mathbb \{F\}_q$ is not $2$ or $3$. We prove that there exist infinitely many $N \in \mathbb \{N\}$ such that the set $\lbrace f \in \mathbb \{F\}_q[t] \colon \deg f < N \rbrace $ contains a Sidon set which is an additive basis of order $3$.},
author = {Kuo, Wentang, Yamagishi, Shuntaro},
journal = {Czechoslovak Mathematical Journal},
keywords = {Sidon set; additive basis; polynomial rings over finite fields},
language = {eng},
number = {2},
pages = {555-562},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Sidon basis in polynomial rings over finite fields},
url = {http://eudml.org/doc/298273},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Kuo, Wentang
AU - Yamagishi, Shuntaro
TI - Sidon basis in polynomial rings over finite fields
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 2
SP - 555
EP - 562
AB - Let $\mathbb {F}_q[t]$ denote the polynomial ring over $\mathbb {F}_q$, the finite field of $q$ elements. Suppose the characteristic of $\mathbb {F}_q$ is not $2$ or $3$. We prove that there exist infinitely many $N \in \mathbb {N}$ such that the set $\lbrace f \in \mathbb {F}_q[t] \colon \deg f < N \rbrace $ contains a Sidon set which is an additive basis of order $3$.
LA - eng
KW - Sidon set; additive basis; polynomial rings over finite fields
UR - http://eudml.org/doc/298273
ER -