We describe the trace representations of two families of binary sequences derived from the
Fermat quotients modulo an odd prime p (one is the binary threshold sequences and the …

On the linear complexity of Hall's sextic residue sequences - Information Theory, IEEE
Transactions on Page 1 2094 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 47 …

Let p=ef+1 be an odd prime for some e and f, and let F_p be the finite field with p elements.
In this paper, we explicitly describe the trace representations of the binary characteristic …

The Legendre symbol is applied to the rational points over an elliptic curve to output a family
of binary sequences with strong pseudorandom properties. That is, both the well-distribution …

We determine the trace function representation, or equivalently, the Fourier spectral
sequences of binary Jacobi sequences of period pq, where p and q are two distinct odd …

We review prime n-square sequences of length pn which is originally defined by Ding and
Helleseth in 1998, where p is an odd prime and n is a positive integer. In this paper, we …

Polyphase versions of the well–known binary Legendre or quadratic–residue sequences
were first described and analysed by Sidelnikov over thirty years ago, but have since …

In this paper, the linear complexity and minimal polynomials of Legendre sequences over F
q have been calculated, where q= pm and p is a prime number. Our results show that …

Let p be a prime with 6∣(p− 1) and integer m⩾ 1. As a generalization of the Hall's sextic
residue sequences, we introduce some families of generalized cyclotomic binary sequences …

PoW consensus can tolerate Byzantine failures by utilizing the cryptographic Hash function
as the mining core. However, there are still risks because attacks on those Hash functions …