Abstract
We determine exact values for the k-error linear complexity L (k) over the finite field F-p of the Legendre sequence L of period p and the Sidelnikov sequence T of period p(m)-1. The results are
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L-k(T)>= min((p+1/2)(m)-1, [p(m)-1/k+1]-(p+1/2)(m) +1)
for 1 <= k <=(p(m)-3)/2 and L-k(T)=0 for k >=(p(m)-1)/2. In particular we prove
L-k(T)=(p+1/2)(m)-1, 1 <= k <= 1/2(3/2)(m)-1.