政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/112102

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政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 > Item 140.119/112102

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/112102

Title:	On the number of solutions of certain diagonal equations over finite fields
Authors:	周文賢 Cao, Xi Wang Chou, Wun Seng Gu, Jingjing
Contributors:	應數系
Keywords:	Finite element method;Covering radius;Cyclic code;Diagonal equation;Finite fields;Gauss sum;Waring`s problem;Algebra
Date:	2016-11
Issue Date:	2017-08-23 10:42:51 (UTC+8)
Abstract:	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
Data Type:	article
DOI 連結:	http://dx.doi.org/10.1016/j.ffa.2016.08.003
DOI:	10.1016/j.ffa.2016.08.003
Appears in Collections:	[應用數學系] 期刊論文

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