New results on periodic sequences with large k-error linear complexity

Niederreiter showed that there is a class of periodic sequences which possess large linear complexity and large k- error linear complexity simultaneously. This result disproved the conjecture that there exists a trade-off between the linear complexity and the k-error linear complexity of a periodic sequence by Ding et al.. Using the entropy function in coding theory, we obtain three main results which hold for much larger k than those of Niederreiter et al.: a) sequences with maximal linear complexity and almost maximal k-error linear complexity with general periods; b) sequences with maximal linear complexity and maximal k-error linear complexity with special periods; c) sequences with maximal linear complexity and almost maximal k-error linear complexity in the asymptotic case with composite periods.