Related papers: Linear Complexity of Binary Interleaved Sequences …
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual $[n,k]$ codes with the largest minimum weight among all binary…
Let $x$ be an $m$-sequence, a maximal length sequence produced by a linear feedback shift register. We show that $x$ has maximal subword complexity function in the sense of Allouche and Shallit. We show that this implies that the…
The run vector of a binary sequence reflects the run structure of the sequence, which is given by the set of all substrings of the run length encoding. The run vector and the aperiodic autocorrelations of a binary sequence are strongly…
Sublinear time algorithms for approximating maximum matching size have long been studied. Much of the progress over the last two decades on this problem has been on the algorithmic side. For instance, an algorithm of Behnezhad [FOCS'21]…
We define a new class of binary matrices by maximizing the peak-sidelobe distances in the aperiodic autocorrelations. These matrices can be used as robust position marks for in-plane spatial alignment. The optimal square matrices of…
Schmidt proved in 2014 that if $\varepsilon>0$, almost all binary sequences of length $n$ have peak sidelobe level between $(\sqrt{2}-\varepsilon)\sqrt{n\log n}$ and $(\sqrt{2}+\varepsilon)\sqrt{n\log n}$. Because of the small gap between…
We study the problem of aligning multiple sequences with the goal of finding an alignment that either maximizes the number of aligned symbols (the longest common subsequence (LCS)), or minimizes the number of unaligned symbols (the…
Let $R$ be a finite commutative chain ring with unique maximal ideal $\langle \gamma\rangle$, and let $n$ be a positive integer coprime with the characteristic of $R/\langle \gamma\rangle$. In this paper, the algebraic structure of cyclic…
We present efficient circuits for the addition of binary numbers. We assume that we are given arrival times for all input bits and optimize the delay of the circuits, i.e.\ the time when the last output bit is computed. This contains the…
Binary sequences are widely used in various practical fields, such as telecommunications, radar technology, navigation, cryptography, measurement sciences, biology or industry. In this paper, a method to generate long binary sequences (LBS)…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
We introduce several new constructions for perfect periodic autocorrelation sequences and arrays over the unit quaternions. This paper uses both mathematical proofs and com- puter experiments to prove the (bounded) array constructions have…
This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…
We Prove That The Uniform Upper Bound for the Number Of Limit Cycles Of The Lienard Equation of Degree 4 Can be equals to 2. Further We Suggest to Embedding Planar Lienard Equations In Higher Dimension and Present question of completly…
In this paper, in order to characterize the critical error linear complexity spectrum (CELCS) for $2^n$-periodic binary sequences, we first propose a decomposition based on the cube theory. Based on the proposed $k$-error cube…
We introduce a construction for families of 2n-dimensional arrays with asymptotically optimal pairwise cross-correlation. These arrays are constructed using a circulant array of n-dimensional Legendre arrays. We also introduce an…
The maximal sum of a sequence "A" of "n" real numbers is the greatest sum of all elements of any strictly contiguous and possibly empty subsequence of "A", and it can be computed in "O(n)" time by means of Kadane's algorithm. Letting "A^(x…
We consider maximum packings of edge-disjoint $4$-cliques in the complete graph $K_n$. When $n \equiv 1$ or $4 \pmod{12}$, these are simply block designs. In other congruence classes, there are necessarily uncovered edges; we examine the…
We formulate learning of a binary autoencoder as a biconvex optimization problem which learns from the pairwise correlations between encoded and decoded bits. Among all possible algorithms that use this information, ours finds the…