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构造了一类新的周期为素数p=4u2+27=6f+1的六次剩余序列,利用有限域和差集理论给出了该序列在周期为素数p≡7mod8情形下的迹函数表示。新序列的线性复杂度为3f=(p-1)2,优于Hall六次剩余序列在相同条件下的线性复杂度。
A new class of six residual sequences with primes p = 4u2 + 27 = 6f + 1 is constructed. By using the theory of finite fields and difference sets, the trace function representation of the sequence in the case of periodic prime p≡7mod8 is given. The linear complexity of the new sequence is 3f = (p-1) 2, which is better than the linear complexity of the remaining sixth order of the Hall under the same conditions.