Related papers: Construction of optimal locally recoverable codes …
It has been a great challenge to construct new quantum MDS codes. In particular, it is very hard to construct quantum MDS codes with relatively large minimum distance. So far, except for some sparse lengths, all known $q$-ary quantum MDS…
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…
In this paper, we consider the convertible code with locally repairable property. We present an improved lower bound on access cost associated with $(r,\delta)$. Then, we provide a general construction of convertible codes with optimal…
We consider the complexities of repair algorithms for locally repairable codes and propose a class of codes that repair single node failures using addition operations only, or codes with addition based repair. We construct two families of…
We study monomial-Cartesian codes (MCCs) which can be regarded as $(r,\delta)$-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to $(r,\delta)$-optimal…
We study error-correcting codes in the space $\mathcal{S}_{n,q}$ of length-$n$ multisets over a $q$-ary alphabet, motivated by permutation channels in which ordering is completely lost and errors act solely by deletions of symbols, i.e., by…
In this work, we give the first construction of high-rate locally list-recoverable codes. List-recovery has been an extremely useful building block in coding theory, and our motivation is to use these codes as such a building block. In…
We prove a general structural theorem for a wide family of local algorithms, which includes property testers, local decoders, and PCPs of proximity. Namely, we show that the structure of every algorithm that makes $q$ adaptive queries and…
In modern storage technologies, symbol-pair codes have emerged as a crucial framework for addressing errors in channels where symbols are read in overlapping pairs to guard against pair errors. A symbol-pair code that meets the…
Locally testable codes (LTC) are error-correcting codes that have a local tester which can distinguish valid codewords from words that are "far" from all codewords by probing a given word only at a very few (sublinear, typically constant)…
We present a simple $q$-ary family of single-error-correcting, double-error-detecting (SEC--DED) linear codes whose parity checks are tied directly to the base-$p$ ($q=p$ prime) digits of the coordinate index. For blocklength $n=p^r$ the…
The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of…
We consider the problem of constructing a code capable of correcting a single long tandem duplication error of variable length. As the main contribution of this paper, we present a $q$-ary efficiently encodable code of length $n+1$ and…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…
This work focuses on sequential locally recoverable codes (SLRCs), a special family of locally repairable codes, capable of correcting multiple code symbol erasures, which are commonly used for distributed storage systems. First, we…
In this work, we construct the first locally-correctable codes (LCCs), and locally-testable codes (LTCs) with constant rate, constant relative distance, and sub-polynomial query complexity. Specifically, we show that there exist binary LCCs…
It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and…
We prove several results on linear codes achieving list-recovery capacity. We show that random linear codes achieve list-recovery capacity with constant output list size (independent of the alphabet size and length). That is, over alphabets…
We prove that 3-query linear locally correctable codes over the Reals of dimension $d$ require block length $n>d^{2+\lambda}$ for some fixed, positive $\lambda >0$. Geometrically, this means that if $n$ vectors in $R^d$ are such that each…
We prove that Reed-Solomon (RS) codes with random evaluation points are list recoverable up to capacity with optimal output list size, for any input list size. Namely, given an input list size $\ell$, a designated rate $R$, and any…