周期序列的k错线性复杂度的期望值(英文)

Expected value of k-error linear complexity of periodic sequences

有限域Fq上一个周期序列的k错线性复杂度被定义为通过改变每个周期至多k个比特所得到的最小线性复杂度.给出有限域Fq上pn周期序列的k错线性复杂度的期望,其中p是一个奇素数,q是模p2的原根,并且1≤k≤(p-1)/2.

The k-error linear complexity of a periodic sequence over a finite field Fq is defined to be the smallest linear complexity that can be obtained by changing k or fewer bits per period. We explicitly give the expected value of k-error linear complexity of p^n-periodic sequences over Fq, where p is an odd prime, q is a prime primitive root modulo p^2, and 1≤k≤ （p -1 ）/2.