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We define the topological complexity sequence of a group as the sequence of topological complexities of its Milnor constructions. This sequence may be regarded as an intrinsic refinement of the topological complexity of a group and, unlike…
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…
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…
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\{…
In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.
We study the $k$-error linear complexity of subsequences of the $d$-ary Sidel'nikov sequences over the prime field $\mathbb{F}_{d}$. A general lower bound for the $k$-error linear complexity is given. For several special periods, we show…
We examine the linear complexity and the autocorrelation properties of new quaternary cyclotomic sequences of period 2p. The sequences are constructed via the cyclotomic classes of order four.
In this paper we present a complete characterization of geometric and linear multiplier sequences for generalized Laguerre bases. In addition, we give a partial characterization of the generic multiplier sequence for such bases, and pose…
In the paper we find effective formulas for the complex geodesics in the symmetrized bidisc.
In this work we introduce a new notion called opacity complexity to measure the complexity of automatic sequences. We study basic properties of this notion, and exhibit an algorithm to compute it. As applications, we compute the opacity…
Binary periodic sequences with good autocorrelation property have many applications in many aspects of communication. In past decades many series of such binary sequences have been constructed. In the application of cryptography, such…
An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
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…
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 determine the symmetrized topological complexity of the circle, using primarily just general topology.
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…
We introduce the new concept of joint nonlinear complexity for multisequences over finite fields and we analyze the joint nonlinear complexity of two families of explicit inversive multisequences. We also establish a probabilistic result on…
We show that the expected value for the linear complexity of $m$-multisequences of length $n$ is E_n^{(m)} = n m/(m+1) + O(1).
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
In this paper, constructions of some double circulant self-dual codes by generalized cyclotomic classes of order two are presented. This technique is applied to [72, 36, 12] binary highest know self-dual codes to obtain self-dual codes over…