Related papers: Optimal $k$-Deletion Correcting Codes

List decoding of insertions and deletions in the Levenshtein metric is considered. The Levenshtein distance between two sequences is the minimum number of insertions and deletions needed to turn one of the sequences into the other. In this…

An edit refers to a single insertion, deletion, or substitution. This paper aims to construct binary codes that can correct two edits. To do this, a necessary and sufficient condition for a code to be two-edit correctable is provided,…

This paper studies on the cardinality of perfect multi deletion binary codes. The lower bound for any perfect deletion code with the fixed code length and the number of deletions, and the asymptotic achievable of Levenshtein's upper bound…

In the paper, the Levenshtein's sequence reconstruction problem is considered in the case where at most $t$ substitution errors occur in each of the $N$ channels and the decoder outputs a list of length $\mathcal{L}$. Moreover, it is…

Determining the largest size, or equivalently finding the lowest redundancy, of q-ary codes for given length and minimum distance is one of the central and fundamental problems in coding theory. Inspired by the construction of…

Motivated by the sequence reconstruction problem initiated by Levenshtein, reconstruction codes were introduced by Cai \emph{et al}. to combat errors when a fixed number of noisy channels are available. The central problem on this topic is…

Batch codes are a useful notion of locality for error correcting codes, originally introduced in the context of distributed storage and cryptography. Many constructions of batch codes have been given, but few lower bound (limitation)…

This paper studies the problem of constructing codes correcting deletions in arrays. Under this model, it is assumed that an $n\times n$ array can experience deletions of rows and columns. These deletion errors are referred to as…

We show the existence of variable-rate rate-distortion codes that meet the disortion constraint almost surely and are minimax, i.e., strongly, universal with respect to an unknown source distribution and a distortion measure that is…

This paper investigates linear-time decoding algorithms for two classes of error-correcting codes. One of the classes is monotone codes which are known as single deletion codes. The other is azinv codes which are known as single balanced…

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…

We introduce the sum channel, a new channel model motivated by applications in distributed storage and DNA data storage. In the error-free case, it takes as input an $\ell$-row binary matrix and outputs an $(\ell+1)$-row matrix whose first…

This paper investigates the problem of correcting multiple criss-cross insertions and deletions in arrays. More precisely, we study the unique recovery of $n \times n$ arrays affected by $t$-criss-cross deletions defined as any combination…

We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a…

This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion…

In this paper, we show that the single deletion correcting Varshamov-Tenengolts code, with minor modifications, can also correct an ordered deletion-erasure pattern where one deletion and at most one erasure occur and the deletion always…

In the Levenshtein's sequence reconstruction problem a codeword is transmitted through $N$ channels and in each channel a set of errors is introduced to the transmitted word. In previous works, the restriction that each channel provides a…

Due to its higher data density, longevity, energy efficiency, and ease of generating copies, DNA is considered a promising storage technology for satisfying future needs. However, a diverse set of errors including deletions, insertions,…

We consider codes over fixed alphabets against worst-case symbol deletions. For any fixed $k \ge 2$, we construct a family of codes over alphabet of size $k$ with positive rate, which allow efficient recovery from a worst-case deletion…

We give a simple algorithm for decremental graph connectivity that handles edge deletions in worst-case time $O(k \log n)$ and connectivity queries in $O(\log k)$, where $k$ is the number of edges deleted so far, and uses worst-case space…