相关论文: On the 2-Adic Complexity of the Ding-Helleseth-Mar…
Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit…
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\{…
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.
Explicit formulas for complexity and unique invariant measure of the period-doubling subshift can be derived from those for the Thue-Morse subshift, obtained by Brlek, De Luca and Varricchio, and Dekking. In this note we give direct proofs…
Let $n_1$ and $n_2$ be two distinct primes with $\mathrm{gcd}(n_1-1,n_2-1)=4$. In this paper, we compute the autocorrelation values of generalized cyclotomic sequence of order $4$. Our results show that this sequence can have very good…
Professor Cunsheng Ding gave cyclotomic constructions of cyclic codes with length being the product of two primes. In this paper, we study the cyclic codes of length $n=2^e$ and dimension $k=2^{e-1}$. Clearly, Ding's construction is not…
Binary Whiteman's cyclotomic sequences of orders 2 and 4 have a number of good randomness properties. In this paper, we compute the autocorrelation values and linear complexity of the first class two-prime Whiteman's generalized cyclotomic…
Binary Sidel'nikov-Lempel-Cohn-Eastman sequences (or SLCE sequences) over F 2 have even period and almost perfect autocorrelation. However, the evaluation of the linear complexity of these sequences is really difficult. In this paper, we…
In this paper, we construct discrete versions of some Bernstein-Gelfand-Gelfand (BGG) complexes, i.e., the Hessian and the divdiv complexes, on triangulations in 2D and 3D. The sequences consist of finite elements with local polynomial…
We analytically solve the constraints in General Relativity for two black holes with arbitrary momenta and spin up to third order in these parameters. We compute the location and geometry of the apparent horizon, which depend on the spins,…
In this paper, a new class of frequency hopping sequences (FHSs) of length $ p^{n} $ is constructed by using Ding-Helleseth generalized cyclotomic classes of order 2, of which the Hamming auto- and cross-correlation functions are…
By using the sieve method of combinatorics, we study $k$-error linear complexity distribution of $2^n$-periodic binary sequences based on Games-Chan algorithm. For $k=4,5$, the complete counting functions on the $k$-error linear complexity…
We investigate the linear complexities of the periodic 0-1 infinite sequences in which the periods are the sequence of the parities of the spacings between quadratic residues modulo a prime p, and the sequence of the parities of the…
We study how the complexity of modular circuits computing AND depends on the depth of the circuits and the prime factorization of the modulus they use. In particular our construction of subexponential circuits of depth 2 for AND helps us to…
From the S-matrix of spinning particles, we extract the 2 PM conservative potential for binary spinning black holes up to quartic order in spin operators. An important ingredient is the exponentiated gravitational Compton amplitude in the…
Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes,…
This paper investigates the dynamical properties of Dickson polynomials over finite fields, focusing on the periodicity and structural behavior of their iterated sequences. We introduce and analyze the sequence $[D_n(x, \alpha) \mod (x^q -…
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity,…
Let l be an odd prime. For primes, p \equiv 1 (mod l), Gauss (l = 3) and Dickson (l = 5) considered the Diophantine systems in terms of which cyclotomic numbers of order 3 and 5 were obtained. The aim of this paper is to show how to obtain…
We obtain divisibility conditions on the multiplicative orders of elements of the form $\zeta + \zeta^{-1}$ in a finite field by exploiting a link to the arithmetic of real quadratic fields.