Related papers: On the $k$-error linear complexity of binary seque…
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 power of an odd prime $p$ for $\mathfrak{r}\geq 2$. When…
We consider the $k$-error linear complexity of a new binary sequence of period $p^2$, proposed in the recent paper "New generalized cyclotomic binary sequences of period $p^2$", by Z. Xiao et al., who calculated the linear complexity of the…
We consider the $k$-error linear complexity of binary sequences derived from Eluer quotients modulo $2p$ ($p>3$ is an odd prime), recently introduced by J. Zhang and C. Zhao. We adopt certain decimal sequences to determine the values of…
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 polynomials and linear complexities are determined…
We continue to investigate binary sequence $(f_u)$ over $\{0,1\}$ defined by $(-1)^{f_u}=\left(\frac{(u^w-u^{wp})/p}{p}\right)$ for integers $u\ge 0$, where $\left(\frac{\cdot}{p}\right)$ is the Legendre symbol and we restrict…
We describe the trace representations of two families of binary sequences derived from Fermat quotients modulo an odd prime $p$ (one is the binary threshold sequences, the other is the Legendre-Fermat quotient sequences) via determining the…
The union cost is used, so that an efficient algorithm for computing the k-error linear complexity of a sequence with period 2pn over GF(q) is presented, where p and q are odd primes, and q is a primitive root of modulo p2.
Let $q=p^r$ be a power of an odd prime $p$. We study binary sequences $\sigma=(\sigma_0,\sigma_1,\ldots)$ with entries in $\{0,1\}$ defined by using the quadratic character $\chi$ of the finite field $\mathbb{F}_q$: $$ \sigma_n=\left\{…
We investigate the $k$-error linear complexity over $\mathbb{F}_p$ of binary sequences of length $2p$ with optimal three-level autocorrelation. These balanced sequences are constructed by cyclotomic classes of order four using a method…
The Euler quotient modulo an odd-prime power $p^r~(r>1)$ can be uniquely decomposed as a $p$-adic number of the form $$ \frac{u^{(p-1)p^{r-1}} -1}{p^r}\equiv a_0(u)+a_1(u)p+\ldots+a_{r-1}(u)p^{r-1} \pmod {p^r},~ \gcd(u,p)=1, $$ where $0\le…
The linear complexity of a sequence has been used as an important measure of keystream strength, hence designing a sequence which possesses high linear complexity and $k$-error linear complexity is a hot topic in cryptography and…
A fast algorithm is presented for determining the linear complexity and the minimal polynomial of periodic sequences over GF(q) with period q n p m, where p is a prime, q is a prime and a primitive root modulo p2. The algorithm presented…
A class of binary sequences with period $2p$ is constructed using generalized cyclotomic classes, and their linear complexity, minimal polynomial over ${\mathbb{F}_{{q}}}$ as well as 2-adic complexity are determined using Gauss period and…
For an odd prime $p$ and an integer $w\ge 1$, polynomial quotients $q_{p,w}(u)$ are defined by $$ q_{p,w}(u)\equiv \frac{u^w-u^{wp}}{p} \bmod p ~~ \mathrm{with}~~ 0 \le q_{p,w}(u) \le p-1, ~~u\ge 0, $$ which are generalizations of Fermat…
In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and…
The linear complexity and k-error linear complexity of a sequence have been used as important measures of keystream strength, hence designing a sequence with high linear complexity and $k$-error linear complexity is a popular research topic…
The linear complexity and the $k$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By studying the linear complexity of binary…
The linear complexity and the $k$-error linear complexity of a binary sequence are important security measures for key stream strength. By studying binary sequences with the minimum Hamming weight, a new tool named as hypercube theory is…
New generalized cyclotomic binary sequences of period $p^2$ are proposed in this paper, where $p$ is an odd prime. The sequences are almost balanced and their linear complexity is determined. The result shows that the proposed sequences…
We determine the exact values of the linear complexity of 2p-periodic quaternary sequences over Z_4 (the residue class ring modulo 4) defined from the generalized cyclotomic classes modulo 2p in terms of the theory of of Galois rings of…