Related papers: Spectrum of Sizes for Perfect Deletion-Correcting …
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
Constructing locally repairable codes achieving Singleton-type bound (we call them optimal codes in this paper) is a challenging task and has attracted great attention in the last few years. Tamo and Barg \cite{TB14} first gave a…
Codes in the Damerau--Levenshtein metric have been extensively studied recently owing to their applications in DNA-based data storage. In particular, Gabrys, Yaakobi, and Milenkovic (2017) designed a length-$n$ code correcting a single…
We consider the problem of constructing binary codes for correcting deletions that are localized within certain parts of the codeword that are unknown a priori. The model that we study is when $\delta \leq w$ deletions are localized in a…
This paper studies codes that correct bursts of deletions. Namely, a code will be called a $b$-burst-deletion-correcting code if it can correct a deletion of any $b$ consecutive bits. While the lower bound on the redundancy of such codes…
In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial…
An $n$-dimensional chair consists of an $n$-dimensional box from which a smaller $n$-dimensional box is removed. A tiling of an $n$-dimensional chair has two nice applications in coding for write-once memories. The first one is in the…
Finding deletion-correcting codes of maximum size has been an open problem for over 70 years, even for a single deletion. In this paper, we propose a novel approach for constructing deletion-correcting codes. A code is a set of sequences…
We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary…
The $q$-ary block codes with two distances $d$ and $d+1$ are considered. Several constructions of such codes are given, as in the linear case all codes can be obtained by a simple modification of linear equidistant codes. Upper bounds for…
In this paper we describe all pairs of binary vectors $({\bf u}, {\bf v})$ such that the set of vectors obtained by $t$ deletions in ${\bf v}$ is a subset of the set of vectors obtained by $t$ deletions in ${\bf u}$ for $t=1,2$. Such pairs…
The main conjecture on maximum distance separable (MDS) codes states that, execpt for some special cases, the maximum length of a q-ary linear MDS code is q+1. This conjecture does not hold true for near maximum distance separable codes…
We consider the problem of correcting insertion and deletion errors in the $d$-dimensional space. This problem is well understood for vectors (one-dimensional space) and was recently studied for arrays (two-dimensional space). For vectors…
This paper studies \emph{linear} and \emph{affine} error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single…
An optimal constant-composition or constant-weight code of weight $w$ has linear size if and only if its distance $d$ is at least $2w-1$. When $d\geq 2w$, the determination of the exact size of such a constant-composition or constant-weight…
The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of…
In this paper, we investigate binary reconstruction codes capable of correcting one deletion and one substitution. We define the \emph{single-deletion single-substitution ball} function $ \mathcal{B} $ as a mapping from a sequence to the…
This paper studies the cardinality of codes correcting insertions and deletions. We give improved upper and lower bounds on code size. Our upper bound is obtained by utilizing the asymmetric property of list decoding for insertions and…
The deletion distance between two binary words $u,v \in \{0,1\}^n$ is the smallest $k$ such that $u$ and $v$ share a common subsequence of length $n-k$. A set $C$ of binary words of length $n$ is called a $k$-deletion code if every pair of…
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. The resulting so-called \emph{Main Problem of Subspace Coding} is to determine the maximum size…