學術產出-期刊論文
| 題名 | On the number of solutions of certain diagonal equations over finite fields |
| 作者 | 周文賢 Cao, Xi Wang Chou, Wun Seng Gu, Jingjing |
| 貢獻者 | 應數系 |
| 關鍵詞 | Finite element method; Covering radius; Cyclic code; Diagonal equation; Finite fields; Gauss sum; Waring`s problem; Algebra |
| 日期 | 2016-11 |
| 上傳時間 | 23-八月-2017 10:42:51 (UTC+8) |
| 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. |
| 關聯 | Finite Fields and their Applications, 42, 225-252 |
| 資料類型 | 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 | 23-八月-2017 10:42:51 (UTC+8) | - |
| dc.date.available | 23-八月-2017 10:42:51 (UTC+8) | - |
| dc.date.issued (上傳時間) | 23-八月-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 |