Abstract: The linear complexity and k-error linear complexity have been used to measure the randomness and the stability of key stream sequences.Both of them are extremely important for studying key stream strength.An effective method to calculate k-error linear complexity is to study error sequences with minimal Hamming weight.On this basis,the counting functions on the 5-error sequences with 5-error linear complexity up to 2^n－3 or equal to 2^n－2－2m,2^n－2－2m+x are derived,and are verified by computer program.

Key words: key stream sequence, k-error linear complexity, k-error sequence