Algorithm for Computing the k-error Linear Complexity and the Corresponding Error Sequence of 2pn-periodic Sequences over GF(q)
NIU Zhihua①② KONG Deyu①
①(School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China) ②(Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai 200444, China)
Abstract：The k-error linear complexity of a sequence is a fundamental concept for assessing the stability of the linear complexity. After computing the k-error linear complexity of a sequence, those bits that make the linear complexity reduced also need to be computed. For 2pn-periodic sequence over GF(q) , where p and q are odd primes and q is a primitive root modulo p2, an algorithm is presented, which not only computes the k-error linear complexity of a sequence s but also gets the corresponding error sequence e. A function is designed to trace the vector cost called “trace function”, so the error sequence e can be computed by calling the “trace function”, and the linear complexity of (s+e) reaches the k-error linear complexity of the sequence s.
牛志华,孔得宇. 计算有限域GF(q)上2pn-周期序列的k-错线性复杂度及其错误序列的算法[J]. 电子与信息学报, 2018, 40(7): 1723-1730.
NIU Zhihua, KONG Deyu. Algorithm for Computing the k-error Linear Complexity and the Corresponding Error Sequence of 2pn-periodic Sequences over GF(q). JEIT, 2018, 40(7): 1723-1730.
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