Two families of Niho sequences having four-valued cross correlation with m-sequences

Cyclic Codes with Four Weights and Sequence Families with Four‐Valued Correlation Functions

“…Remark 2 Theorem 1 generalizes the results of Theorem 1 in Ref. [16] and part results of Theorem 23 in Ref. [14].…”

“…[14] and Ref. [16] was extended and under more flexible conditions, the value distribution of an exponential sum was completely determined. As applications, the weight distribution of a class of four-weight cyclic codes with parameters [2 n − 1, 2n, 2 n−1 − 2 m+gcd(s,m)−1 ] was presented, and some of the cyclic codes have the best known parameters.…”

“…Lemma 3 (Lemma 2.2 in Ref. [16]) Let v 2 (t) denote the highest power 2 dividing t, and k, l be positive integers. Then…”

“…[14]. In a recent paper [16] , the value distribution of S(a, b) is also determined under the conditions v 2 (s) = v 2 (m) = 0 and gcd(s, m) = 1. Hence, in some extend the present paper is a generalization of the work Ref.…”

Two Families of Optimal Ternary Cyclic Codes With Two Zeros

“…Lemma 4: (Theorems 2.4 and 2.6 in [20]) Let a, t and l be positive integers. Then is even and a is odd a gcd(t,l) + 1, if both t gcd(t,l) and l gcd(t,l) are odd.…”