相关论文: Duplication Distance to the Root for Binary Sequen…
We investigate the asymptotic rates of length-$n$ binary codes with VC-dimension at most $dn$ and minimum distance at least $\delta n$. Two upper bounds are obtained, one as a simple corollary of a result by Haussler and the other via a…
This work studies problems in data reconstruction, an important area with numerous applications. In particular, we examine the reconstruction of binary and non-binary sequences from synchronization (insertion/deletion-correcting) codes.…
We define sequence patterns of length $n$ and level $\ell$ to be equivalence classes of sequences that have $n$ elements from the set of $\ell$ integer symbols $\{1,2,\ldots,\ell\}$ with no restriction on repetition, where the equivalence…
Consider the problem of finding high dimensional approximate nearest neighbors, where the data is generated by some known probabilistic model. We will investigate a large natural class of algorithms which we call bucketing codes. We will…
It is an open question whether there exists a polynomial-time algorithm for computing the rotation distances between pairs of extended ordered binary trees. The problem of computing the rotation distance between an arbitrary pair of trees,…
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…
The problem of similarity search is one of the main problems in computer science. This problem has many applications in text-retrieval, web search, computational biology, bioinformatics and others. Similarity between two data objects can be…
A two-dimensional string is simply a two-dimensional array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs.…
The Hamming oracle returns the Hamming distance between an unknown binary $n$-vector $x$ and a binary query $n$-vector y. The objective is to determine $x$ uniquely using a sequence of $m$ queries. What are the minimum number of queries…
Various approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between two input sequences. Haubold {\em et al.} (2009) showed how the average number of substitutions between two DNA…
Binary sequences with minimal autocorrelations have applications in communication engineering, mathematics and computer science. In statistical physics they appear as groundstates of the Bernasconi model. Finding these sequences is a…
We propose a fast, distance-preserving, binary embedding algorithm to transform a high-dimensional dataset $\mathcal{T}\subseteq\mathbb{R}^n$ into binary sequences in the cube $\{\pm 1\}^m$. When $\mathcal{T}$ consists of well-spread (i.e.,…
Finding the most similar subsequences between two multidimensional time series has many applications: e.g. capturing dependency in stock market or discovering coordinated movement of baboons. Considering one pattern occurring in one time…
We describe a kernel of size 9k-8 for the NP-hard problem of computing the Tree Bisection and Reconnect (TBR) distance k between two unrooted binary phylogenetic trees. We achieve this by extending the existing portfolio of reduction rules…
Recently we considered a class of random matrices obtained by choosing distinct codewords at random from linear codes over finite fields and proved that under some natural algebraic conditions their empirical spectral distribution converges…
In a recent remarkable paper, Babadi and Tarokh proved the "randomness" of sequences arising from binary linear block codes in the sense of spectral distribution, provided that their dual distances are sufficiently large. However, numerical…
Binary cyclic codes having large dimensions and minimum distances close to the square-root bound are highly valuable in applications where high-rate transmission and robust error correction are both essential. They provide an optimal…
The $2$-adic complexity has been well-analyzed in the periodic case. However, we are not aware of any theoretical results on the $N$th $2$-adic complexity of any promising candidate for a pseudorandom sequence of finite length $N$ or…
The Levenshtein sequence reconstruction problem studies the reconstruction of a transmitted sequence from multiple erroneous copies of it. A fundamental question in this field is to determine the minimum number of erroneous copies required…
All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…