Explicit Full Correlation Distribution of Sequence Families Using Plateaued Functions

Correlation distribution of a sequence family generalizing some sequences of Trachtenberg

“…Later, Boztaş,Özbudak and Tekin studied the sequence family V when g(x) is the Kasami function and obtained its full and exact correlation distribution [3]. The results of Theorem 3 in [5] are a special subcase for the family V, which is given in Case 3, Proof of Theorem 21 in [3]. Recall that, all these results are obtained when the characteristic p is 2.…”

“…Plateaued functions are closely related to sequence design. Boztaş,Özbudak and Tekin [3] studied a general sequence family V = {v i (t) : i = 1, 2, ..., p n + 1}, where every element of this family is defined as v i (t) =…”

“…Specifically, when p = 2, the exact correlation values were obtained under the same restrictions. Further information can be found in Theorem 16 of [3]. Additionally, they computed the approximate correlation distribution of the function g(x) = Tr(x 1+p ) for all n values when p is odd and exact correlation distribution when p = 2, using Theorem 16 and some techniques on algebraic curves [3].…”

“…Further information can be found in Theorem 16 of [3]. Additionally, they computed the approximate correlation distribution of the function g(x) = Tr(x 1+p ) for all n values when p is odd and exact correlation distribution when p = 2, using Theorem 16 and some techniques on algebraic curves [3]. Kasami functions, which are e-plateaued functions, have been generated in even characteristic under some restrictions on n where d = 2 2k −2 k +1 and gcd(n, k) = e. The correlation of the Kasami function g(x) = Tr(x d ) with linear m-sequences was given in Theorem 3, Appendix A of [5] and attributed to Lloyd R. Welch [10,12].…”

“…Kasami functions, which are e-plateaued functions, have been generated in even characteristic under some restrictions on n where d = 2 2k −2 k +1 and gcd(n, k) = e. The correlation of the Kasami function g(x) = Tr(x d ) with linear m-sequences was given in Theorem 3, Appendix A of [5] and attributed to Lloyd R. Welch [10,12]. Later, Boztaş,Özbudak and Tekin studied the sequence family V when g(x) is the Kasami function and obtained its full and exact correlation distribution [3]. The results of Theorem 3 in [5] are a special subcase for the family V, which is given in Case 3, Proof of Theorem 21 in [3].…”