We show that a p-ary polyphase sequence of period p 2 from the Fermat quotients is perfect.
That is, its periodic autocorrelation is zero for all non-trivial phase shifts. We call this Fermat …

We investigate the $ k $-error linear complexity of $ p^ 2$-periodic binary sequences
defined from the polynomial quotients (including the well-studied Fermat quotients), which is …

We give the trace representation of a family of binary sequences derived from Euler
quotients by determining the corresponding defining polynomials. The result extends an …

An m-sequence is the one of the largest period among those produced by a linear feedback
shift register. It possesses several desirable features of pseudorandomness such as …

We investigate the $ k $-error linear complexity of pseudorandom binary sequences of
period $ p^{\mathfrak {r}} $ derived from the Euler quotients modulo $ p^{\mathfrak {r}-1} $, a …

Carmichael quotients for an integer m ≥ 2 m≥ 2 are introduced analogous to Fermat
quotients, by using Carmichael function λ (m) λ (m). Various properties of these new …

We consider the k-error linear complexity of a new generalized cyclotomic binary sequence
of period p 2 for an odd prime p. The new sequences were introduced recently by Z. **ao, X …

Let p= ef+ 1 be an odd prime, where e≡ 0 (mod 4). A family of balanced quaternary
sequences is defined by using the classical cyclotomic classes of order e with respect to p in …

We first introduce a family of binary pq 2-periodic sequences based on the Euler quotients
modulo pq, where p and q are two distinct odd primes and p divides q-1. The minimal …

Linear Complexity and Trace Presentation of Sequences with Period 2P2 Page 1 Linear
complexity and trace presentation of sequences with period 2p 2 1st **gwei Zhang School of …