Related papers: On de Bruijn Array Codes Part II: Linear Codes
Line-of-sight (LoS) multiple-input multiple-output (MIMO) gives full spatial-multiplexing gain when the antenna array geometry and orientation are designed based on the inter-terminal distance. These known design methodologies, that hold…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
Recently, two-dimensional (2D) array codes have been found to have applications in wireless communication.In this paper, we propose direct construction of 2D complete complementary codes (2D-CCCs) with arbitrary array size and flexible set…
The skew of a binary string is the difference between the number of zeroes and the number of ones, while the length of the string is the sum of these two numbers. We consider certain suffixes of the lexicographically-least de Bruijn…
Locality-sensitive hashing (LSH) is a popular data-independent indexing method for approximate similarity search, where random projections followed by quantization hash the points from the database so as to ensure that the probability of…
We revisit the pseudo-random sequence introduced by Ehrenfeucht and Mycielski and its connections with DeBruijn strings.
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
We are studying here the classical operator creating secondary polynomials associated with an orthogonal system for a continuous probability density function on a real interval. We know it is possible with the coupling of Stietjes…
We define a model for random (abstract) cell complexes (CCs), similiar to the well-known Erd\H{o}s-R\'enyi model for graphs and its extensions for simplicial complexes. To build a random cell complex, we first draw from an Erd\H{o}s-R\'enyi…
Sidon sequences and their generalizations have found during the years and especially recently various applications in coding theory. One of the most important applications of these sequences is in the connection of synchronization patterns.…
A scheme for pseudo-random binary sequence generation based on the two-dimensional discrete-time Henon map is proposed. Properties of the proposed sequences pertaining to linear complexity, linear complexity profile, correlation and…
A de Bruijn covering code is a q-ary string S so that every q-ary string is at most R symbol changes from some n-word appearing consecutively in S. We introduce these codes and prove that they can have length close to the smallest possible…
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…
Given an alphabet $S$, we consider the size of the subsets of the full sequence space $S^{\rm {\bf Z}}$ determined by the additional restriction that $x_i\not=x_{i+f(n)},\ i\in {\rm {\bf Z}},\ n\in {\rm {\bf N}}.$ Here $f$ is a positive,…
De Bruijn tori, or perfect maps, are two-dimensional periodic arrays of letters from a finite alphabet, where each possible pattern of shape (m,n) appears exactly once in a single period. While the existence of certain de Bruijn tori, such…
Long linear codes constructed from toric varieties over finite fields, their multiplicative structure and decoding. The main theme is the inherent multiplicative structure on toric codes. The multiplicative structure allows for…
Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued…
We introduce a new concept of a subgraph class called a superbubble for analyzing assembly graphs, and propose an efficient algorithm for detecting it. Most assembly algorithms utilize assembly graphs like the de Bruijn graph or the overlap…
The paper study counter-dependent pseudorandom generators; the latter are generators such that their state transition function (and output function) is being modified dynamically while working: For such a generator the recurrence sequence…
Prompted by a question of Jim Propp, this paper examines the cyclic sieving phenomenon (CSP) in certain cyclic codes. For example, it is shown that, among dual Hamming codes over $F_q$, the generating function for codedwords according to…