We establish the existence of periodic sequences over a finite field which simultaneously achieve the maximum value (for the given period length) of the linear complexity and of the k-error linear complexity for small values of k. This disproves a conjecture of Ding, Xiao, and Shan (1991). The result is of relevance for the theory of stream ciphers.
['Harald Niederreiter']
Periodic sequences with large k-error linear complexity