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TitleOn 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 WordsFinite element method; Covering radius; Cyclic code; Diagonal equation; Finite fields; Gauss sum; Waring`s problem; Algebra
Date2016-11
Date Issued23-Aug-2017 10:42:51 (UTC+8)
SummaryWe 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.
RelationFinite Fields and their Applications, 42, 225-252
Typearticle
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 Wangen_US
dc.creator (作者) Chou, Wun Sengen_US
dc.creator (作者) Gu, Jingjingen_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 fieldsen_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