Kim et al. determined the trace function representation of Legendre sequences with prime period p ≡ 3 or - 3 (mod 8) by using two different primitive elements of the finite field GF(2^n) .In this correspondence,firstly,the authors divide the group GF(p) * into the union of cosets of subgroup generated by 4. Then, they propose a new trace function representation of Legendre sequences via the trace function from the finite field GF(2^n ) to its subfield GF(4 ). The trace representation is described only using one primitive element of the finite field GF(2^n). It has positive effect to the computational implementation of Legendre sequences.%当素数p=3或-3(mod 8)时,Kim等利用有限域GF(2n)中两个不同的本原元刻画了周期为p的Leg-endre序列的迹表示.本文通过分割有限域的乘法群GF(p)*关于元素4生成的子群的陪集,利用从GF(2n)到子域GF(4)的迹函数,提出Legendre序列的一种新的迹表示形式.该结论仅用GF(2n)中的一个本原元即可确定序列,对其计算实现有积极的意义.
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