Related papers: Structure Analysis on the $k$-error Linear Complex…
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 generalized binary sequences of order 2 have been used to construct good binary cyclic codes [4]. The linear complexity of these sequences has been computed in [2]. The autocorrelation values of such sequences have been determined in…
The linear complexity (LC) of a sequence has been used as a convenient measure of the randomness of a sequence. Based on the theories of linear complexity, $k$-error linear complexity, the minimum error and the $k$-error linear complexity…
In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the…
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
This paper introduces a novel method for compact representation of sets of n-dimensional binary sequences in a form of compact triplets structures (CTS), supposing both logic and arithmetic interpretations of data. Suitable illustration of…
We compare ordinary and symmetric variants of two classical measures of pseudorandomness for binary sequences, the $2$-adic complexity and the linear complexity. In the periodic setting, we show that for binary periodic sequences…
A method for efficiently successive cancellation (SC) decoding of polar codes with high-dimensional linear binary kernels (HDLBK) is presented and analyzed. We devise a $l$-expressions method which can obtain simplified recursive formulas…
We present an approach to showing that a linear code is resilient to random errors. We use this approach to obtain decoding results for both transitive codes and Reed-Muller codes. We give three kinds of results about linear codes in…
Finding dense components in graphs is of great importance in analyzing the structure of networks. Popular and computationally feasible frameworks for discovering dense subgraphs are core and truss decompositions. Recently, Sariyuce et al.…
Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general,…
We study finding and listing $k$-cliques in a graph, for constant $k\geq 3$, a fundamental problem of both theoretical and practical importance. Our main contribution is a new output-sensitive algorithm for listing $k$-cliques in graphs,…
In this paper, we propose a partitioning technique that decomposes a pair of sequences with overlapping $t$-deletion $s$-substitution balls into sub-pairs, where the $^{\leq}t$-burst-deletion balls of each sub-pair intersect. This…
Set classification aims to classify a set of observations as a whole, as opposed to classifying individual observations separately. To formally understand the unfamiliar concept of binary set classification, we first investigate the optimal…
In the first paper of this series we presented EBAS, a new fully automated algorithm to analyse the lightcurves of eclipsing binaries, based on the EBOP code. Here we apply the new algorithm to the whole sample of 2580 binaries found in the…
The Subset Feedback Vertex Set problem (SFVS), to delete $k$ vertices from a given graph such that any vertex in a vertex subset (called a terminal set) is not in a cycle in the remaining graph, generalizes the famous Feedback Vertex Set…
We propose a new technique for consistent estimation of the number and locations of the change-points in the structure of an irregularly spaced time series. The core of the segmentation procedure is the Ensemble Binary Segmentation method…
We study the construction of $d$-deletion-correcting binary codes by formulating the problem as a Maximum Clique Problem (MCP). In this formulation, vertices represent candidate codewords and edges connect pairs whose longest common…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…