CAJ | 학술논문

给出了一个快速算法决定有限域Fq上周期为upn序列的极小多项式.设p,q,u为不同素数,q为模p2的本原根,m为最小正整数使得qm≡1modu和gcd(m,p(p-1))=1.利用一个算法把有限域Fq上周期为upn序列化为几个有限域Fq(ζ)上周期为pn序列,其中ζ为一个u次本原单位根,从而利用肖国正等的算法得到每个周期为pn序列的极小多项式.
급출료일개쾌속산법결정유한역Fq상주기위upn서렬적겁소다항식.설p,q,u위불동소수,q위모p2적본원근,m위최소정정수사득qm≡1modu화gcd(m,p(p-1))=1.이용일개산법파유한역Fq상주기위upn서렬화위궤개유한역Fq(ζ)상주기위pn서렬,기중ζ위일개u차본원단위근,종이이용초국정등적산법득도매개주기위pn서렬적겁소다항식.
A fast algorithm for determining the minimal polynomial and linear complexity of a upn-periodic sequence over a finite field Fq is given.Let p,q,and u be distinct primes,q a primitive root modulo p2,m the smallest positive integer such that qm(＝)1 mod u,and gcd(m,p(p - 1)) =1.An algorithm is used to reduce a periodic upn sequence over Fq to several pn-periodic sequences over Fq (ζ),where ζ is a u-th primitive root of unity,and an algorithm proposed by Xiao et al.is employed to obtain the minimal polynomial of each pnperiodic sequence.