No abstract

Cryptographic sequences with high linear complexity and high k-error linear complexity are called excellent sequences. In this paper, we design a genetic algorithm to generate an excellent -periodic binary sequence. With the genetic algorithm, we do some numerical experiments to study the character of the excellent sequences. We get some interesting results when k satisfies = ( < < ), and give a conjecture that excellent sequences with = ( < < ) have a highest k-error linear complexity related to the period and k.