Research on Excellent p^n-periodic Binary Sequence with Genetic Algorithm

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 pⁿ-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 k = p^r(0 <; r <; n), and give a conjecture that excellent sequences with k = p^r(0 <; r <; n) have a highest k-error linear complexity related to the period and k.