Related papers: An Efficiently Generated Family of Binary de Bruij…
Due to wide applications of binary sequences with low correlation to communications, various constructions of such sequences have been proposed in literature. However, most of the known constructions via finite fields make use of the…
We introduce and analyze an efficient family of linear feedback shift registers (LFSR's) with maximal period. This family is word-oriented and is suitable for implementation in software, thus provides a solution to a recent challenge posed…
We study an interesting family of cooperating coroutines, which is able to generate all patterns of bits that satisfy certain fairly general ordering constraints, changing only one bit at a time. (More precisely, the directed graph of…
A balanced generalized de Bruijn sequence with parameters $(n,l,k)$ is a cyclic sequence of $n$ bits such that (a) the number of 0's equals the number of 1's, and (b) each substring of length $l$ occurs at most $k$ times. We determine…
Classic cycle-joining techniques have found widespread application in creating universal cycles for a diverse range of combinatorial objects, such as shorthand permutations, weak orders, orientable sequences, and various subsets of $k$-ary…
One of the fundamental ways to construct De Bruijn sequences is by using a shift-rule. A shift-rule receives a word as an argument and computes the symbol that appears after it in the sequence. An optimal shift-rule for an $(n,k)$-De Bruijn…
A binary modified de Bruijn sequence is an infinite and periodic binary sequence derived by removing a zero from the longest run of zeros in a binary de Bruijn sequence. The minimal polynomial of the modified sequence is its unique…
A special type of cyclic sequences named adjacency-hopping de Bruijn sequences is introduced in this paper. It is theoretically proved the existence of such sequences, and the number of such sequences is derived. These sequences guarantee…
The well known prefer-one, prefer-opposite, and prefer-same binary de Bruijn sequences are all constructed using simple preference rules. We apply the technique of preference functions of span one to define q-ary sequences that generalize…
A shift rule for the prefer-max De Bruijn sequence is formulated, for all sequence orders, and over any finite alphabet. An efficient algorithm for this shift rule is presented, which has linear (in the sequence order) time and memory…
Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details.…
We present an algebraic construction of trace-based De Bruijn tori over finite fields, focusing on the nonzero variant that omits the all-zero pattern. The construction arranges nonzero field elements on a toroidal grid using two…
We propose a new efficient iterative method for generating random correlated binary sequences with prescribed correlation function. The method is based on consecutive linear modulations of initially uncorrelated sequence into a correlated…
We present an algorithm for effectively generating binary sequences which would be rated by people as highly likely to have been generated by a random process, such as flipping a fair coin.
In the realm of modern digital communication, cryptography, and signal processing, binary sequences with a low correlation properties play a pivotal role. In the literature, considerable efforts have been dedicated to constructing good…
The de Bruijn torus (or grid) problem looks to find an $n$-by-$m$ binary matrix in which every possible $j$-by-$k$ submatrix appears exactly once. The existence and construction of these binary matrices was determined in the 70's, with…
A de Bruijn sequence of order $k$ over a finite alphabet is a cyclic sequence with the property that it contains every possible $k$-sequence as a substring exactly once. Orthogonal de Bruijn sequences are collections of de Bruijn sequences…
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)…
Sequences with a low correlation have very important applications in communications, cryptography, and compressed sensing. In the literature, many efforts have been made to construct good sequences with various lengths where binary…
The use of three extractors, fed by linear feedback shift registers (LFSR) for generating pseudo-random bit streams is investigated. Specifically, a standard LFSR is combined with a von Neumann extractor, a modified LFSR, extended by the…