Related papers: The 2-adic complexity of a class of binary sequenc…
We study ternary sequences associated with a multidimensional continued fraction algorithm introduced by the first author. The algorithm is defined by two matrices and we show that it is measurably isomorphic to the shift on the set…
Binary sequences with lower autocorrelation values have important applications in cryptography and communications. In this paper, we present all possible parameters for binary periodical sequences with a 2-level autocorrelation values. For…
Building on previous results of Xing, we give new lower bounds on the rate of intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry, although nothing beyond the basic theory of linear systems on…
In this paper we study almost $p$-ary sequences and their autocorrelation coefficients. We first study the number $\ell$ of distinct out-of-phase autocorrelation coefficients for an almost $p$-ary sequence of period $n+s$ with $s$…
In \cite{shi2022few-weight}, Shi and Li studied $\mathcal{C}_D$-codes over the ring $\mathcal{R}:=\mathbb{F}_2[x,y]/\langle x^2, y^2, xy-yx\rangle$ and their binary Gray images, where $D$ is derived using certain simplicial complexes. We…
Binary sequences with optimal autocorrelation play important roles in radar, communication, and cryptography. Finding new binary sequences with optimal autocorrelation has been an interesting research topic in sequence design.…
We study networked binary classification on a directed acyclic graph (DAG) where each agent observes only a subset of the feature columns of a shared dataset. Agents act sequentially along the DAG: each receives prediction columns from its…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
We study the robust communication complexity of maximum matching. Edges of an arbitrary $n$-vertex graph $G$ are randomly partitioned between Alice and Bob independently and uniformly. Alice has to send a single message to Bob such that Bob…
Pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that, when compared to random sequence pairs, simultaneously achieve significantly lower mean square autocorrelation…
Secret sharing is an important building block in cryptography. All explicitly defined secret sharing schemes with known exact complexity bounds are multi-linear, thus are closely related to linear codes. The dual of such a linear scheme, in…
Constructions of binary sequences with low autocorrelation are considered in the paper. Based on recent progresses about this topic, several more general constructions of binary sequences with optimal autocorrelations and other low…
In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
We study the one-way two-party communication complexity of Maximum Matching in the semi-robust setting where the edges of a maximum matching are randomly partitioned between Alice and Bob, but all remaining edges of the input graph are…
Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there have been significant advancements in the topic of complexity measures for randomness assessment, which are of fundamental importance in theoretical…
In this paper three Schur ring are discussed, namenly: Hamming, circulant orbists and decimated circulant orbits Schur ring. By using autocorrelation function and the run structure of binary sequences we proof the relation between this…
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion…
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 merit factor of a $\{-1, 1\}$ binary sequence measures the collective smallness of its non-trivial aperiodic autocorrelations. Binary sequences with large merit factor are important in digital communications because they allow the…
The Longest Common Subsequence (LCS) is a fundamental string similarity measure, and computing the LCS of two strings is a classic algorithms question. A textbook dynamic programming algorithm gives an exact algorithm in quadratic time, and…