CAJ | 학술논문

针对广义割圆序列的构造问题，提出周期为pm的任意阶广义割圆序列的构造方法，应用有限域GF(2)上多项式根的理论，分析该类序列线性复杂度所有可能的取值。结果表明，该序列具有较好的线性复杂度，能抗击B-M算法，可用于推广现有的周期为pm序列的相关研究，并对已有文献中的部分错误证明进行订正。
침대엄의할원서렬적구조문제，제출주기위pm적임의계엄의할원서렬적구조방법，응용유한역GF(2)상다항식근적이론，분석해류서렬선성복잡도소유가능적취치。결과표명，해서렬구유교호적선성복잡도，능항격B-M산법，가용우추엄현유적주기위pm서렬적상관연구，병대이유문헌중적부분착오증명진행정정。
According to the construction of generalized cyclotomic sequences, this paper propose a construction method of generalized cyclotomic sequences with period pm of arbitrary order. It uses the theory of polynomial root over finite fields GF(2). All the possible values of linear complexity of sequences are obtained. Results show that the new sequence has larger linear complexity and can resist the attack by B-M algorithm. The sequence generalizes the existed construction, and also revises some incorrect proof in the literature.