On the number of solutions of certain diagonal equations over finite fields

Title	On the number of solutions of certain diagonal equations over finite fields
Creator	周文賢 Cao, Xi Wang Chou, Wun Seng Gu, Jingjing
Contributor	應數系
Key Words	Finite element method; Covering radius; Cyclic code; Diagonal equation; Finite fields; Gauss sum; Waring`s problem; Algebra
Date	2016-11
Date Issued	23-Aug-2017 10:42:51 (UTC+8)
Summary	We use character sums over finite fields to give formulas for the number of solutions of certain diagonal equations of the forma1x1 m1+a2x2 m2+⋯+anxn mn=c. We also show that if the value distribution of character sums ∑x∈Fqχ(axm+bx), a,b∈Fq, is known, then one can obtain the number of solutions of the system of equations{x1+x2+⋯+xn=αx1 m+x2 m+⋯+xn m=β for some particular m. We finally apply our results to induce some facts about Waring`s problems and the covering radius of certain cyclic codes.
Relation	Finite Fields and their Applications, 42, 225-252
Type	article
DOI	http://dx.doi.org/10.1016/j.ffa.2016.08.003

dc.contributor	應數系
dc.creator (作者)	周文賢	zh_tw
dc.creator (作者)	Cao, Xi Wang	en_US
dc.creator (作者)	Chou, Wun Seng	en_US
dc.creator (作者)	Gu, Jingjing	en_US
dc.date (日期)	2016-11
dc.date.accessioned	23-Aug-2017 10:42:51 (UTC+8)	-
dc.date.available	23-Aug-2017 10:42:51 (UTC+8)	-
dc.date.issued (上傳時間)	23-Aug-2017 10:42:51 (UTC+8)	-
dc.identifier.uri (URI)	http://nccur.lib.nccu.edu.tw/handle/140.119/112102	-
dc.description.abstract (摘要)	We use character sums over finite fields to give formulas for the number of solutions of certain diagonal equations of the forma1x1 m1+a2x2 m2+⋯+anxn mn=c. We also show that if the value distribution of character sums ∑x∈Fqχ(axm+bx), a,b∈Fq, is known, then one can obtain the number of solutions of the system of equations{x1+x2+⋯+xn=αx1 m+x2 m+⋯+xn m=β for some particular m. We finally apply our results to induce some facts about Waring`s problems and the covering radius of certain cyclic codes.
dc.format.extent	209 bytes	-
dc.format.mimetype	text/html	-
dc.relation (關聯)	Finite Fields and their Applications, 42, 225-252
dc.subject (關鍵詞)	Finite element method; Covering radius; Cyclic code; Diagonal equation; Finite fields; Gauss sum; Waring`s problem; Algebra
dc.title (題名)	On the number of solutions of certain diagonal equations over finite fields	en_US
dc.type (資料類型)	article
dc.identifier.doi (DOI)	10.1016/j.ffa.2016.08.003
dc.doi.uri (DOI)	http://dx.doi.org/10.1016/j.ffa.2016.08.003