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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
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Appears in Collections:[應用數學系] 期刊論文

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