周期为2p^n的q元序列m紧错线性复杂度

m-Tight Error Linear Complexity of Sequences with Period 2p^n over GF(q)

结合k错线性复杂度曲线和最小错误的理论,提出m紧错线性复杂度的概念来研究序列线性复杂度的稳定性.首先优化魏-肖-陈算法的结构,即GF(q)上求周期为2pn的q元序列线性复杂度的快速算法;然后通过采用联合代价的方法,给出一个GF(q)上求周期为2pn的q元序列k错线性复杂度的快速算法;接着给出周期为2pn的q元序列的m紧错线性复杂度快速算法,其中p和q是奇素数,q为模p2的一个本原根.

Using the theories of the minimum error and the k-error linear complexity profile of sequences,m-tight error linear complexity is presented to study the stability of the linear complexity of sequences.First,the structure of the Wei-Xiao-Chen algorithm for the linear complexity of sequences with period 2pn over GF(q) is optimized,where p and q are odd primes and q is a primitive root(mod p2).Second,the union cost is used,so that an efficient algorithm for computing the k-error linear complexity of a sequence with period 2pn over GF(q) is derived,where p and q are odd primes and q is a primitive root(mod p2).Finally,an efficient algorithm for computing m-tight error linear complexity of sequences with period 2pn over GF(q) is given,where p and q are odd primes and q is a primitive root(mod p2).