有限域上三项式的本原性(英文)  

On the Primitivity of Some Trinomials Over Finite Fields

作　　者：李玉娟 王怀富 赵进华 

机构地区：[1]信息保障技术重点实验室,北京100072

出　　处：《数学进展》2015年第3期387-393,共7页Advances in Mathematics（China）

摘　　要：给出了有限域F_(pm)上形式为x^2+ax+b的三项式非本原的条件,进而给出有限域F_(pm)上不存在形式为x^n+ax+b的三项式的条件.特别地,对有限域F_4,证明了三项式x^n+ax+b只可能在n等于2,或者n模30等于5或11时本原.In this paper,we give conditions under which the trinomials of the form x^n +ax + b over finite field F_pm are not primitive and conditions under which there are no primitive trinomials of the form x^n + ax + b over finite field F_(pm).Specially for finite field F4,we show that the trinomials of the form x^n + ax + b can not be primitive over F4 except possibly for n = 2,n = 5(mod 30) or n = 11(mod 30).

关 键 词：有限域 线性递归序列 本原三项式 

分 类 号：O153.4[理学—数学]