An algorithm for the 𝒦-error linear complexity of a sequence with period 2𝑝𝑛 over GF( 𝑞)

We first optimize the structure of the
Wei-Xiao-Chen
algorithm for the linear complexity of sequences over
GF(q)
with period
N = 2pⁿ,
where
p
and
q
are odd primes, and
q
is a primitive root
( mod p²)
. Then the union cost is used, so that an efficient algorithm for computing k-error linear complexity of a sequence with period
2pⁿ,
over
GF(q)
is derived, where
p
and
q
are odd primes, and
q
is a primitive root of modulo
p²
. We also give a validity proof of the proposed algorithm. Finally, a numerical example is presented to illustrate the algorithm.