Trace Representation and Linear Complexity of Binary $e$th Power Residue Sequences of Period $p$

About computation of the linear complexity of generalized cyclotomic sequences with period p n+1

“…In [15] the values of the polynomial T (x) are computed depending on x, y. This also can be obtained using the approach proposed in [17,18]. Without breaking the integrity we can presume that T (β) = 0 and let T(β) = T (β), T (β g ), .…”

A trace representation of binary Jacobi sequences

“…As an easy consequence, we determine the linear complexity of the sequence which was obtained earlier [5,13]. The result in this paper makes use of the results in both [14,4].…”

“…We call the pair (g(x), γ ) a defining pair of the sequence s [4]. In the remainder of this paper, we will consider only the case where N is either an odd prime or a product of two distinct odd primes.…”

“…It is well known that F * p is a disjoint union of A 0 {x 2 |x ∈ F * p } and A 1 F * p \ A 0 of equal size ( p − 1)/2. It is also well known that A 0 is a cyclic difference set with parameters (v = p, k = ( p − 1)/2, λ = ( p − 3)/4) [1,4,9,11,12,14]. In the remainder of this paper, we let…”

On the linear complexity of Hall’s sextic residue sequences over $${ GF}(q)$$ G F ( q )

“…The linear complexity of Hall's sextic residue sequences with the length p was considered in [14] over the finite field of order 2 and in [1] over the finite field of p elements. The linear complexity of other binary cyclotomic sequences of order 6 over the finite field of order 2 was investigated in [3,7,15] (also, see references therein). Further, the linear complexity of series of generalized cyclotomic sextic sequences over the finite field of order 2 was studied in [6,8].…”