Related papers: Non-binary Two-Deletion Correcting Codes and Burst…
In recent years, several classes of codes are introduced to provide some fault-tolerance and guarantee system reliability in distributed storage systems, among which locally repairable codes (LRCs for short) play an important role. However,…
Guess & Check (GC) codes are systematic binary codes that can correct multiple deletions, with high probability. GC codes have logarithmic redundancy in the length of the message $k$, and the encoding and decoding algorithms of these codes…
A quasi-Gray code of dimension $n$ and length $\ell$ over an alphabet $\Sigma$ is a sequence of distinct words $w_1,w_2,\dots,w_\ell$ from $\Sigma^n$ such that any two consecutive words differ in at most $c$ coordinates, for some fixed…
A locally repairable code with availability has the property that every code symbol can be recovered from multiple, disjoint subsets of other symbols of small size. In particular, a code symbol is said to have $(r,t)$-availability if it can…
A decoding algorithm for $q$-ary low-density parity-check codes over the $q$-ary symmetric channel is introduced. The exchanged messages are lists of symbols from $\Fq$. A density evolution analysis for maximum list sizes $1$ and $2$ is…
We examine and compare several different classes of "balanced" block codes over q-ary alphabets, namely symbol-balanced (SB) codes, charge-balanced (CB) codes, and polarity-balanced (PB) codes. Known results on the maximum size and…
Function-correcting codes, introduced by Lenz, Bitar, Wachter-Zeh, and Yaakobi, protect specific function values of a message rather than the entire message. A central challenge is determining the optimal redundancy -- the minimum…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction…
Distributed storage systems need to store data redundantly in order to provide some fault-tolerance and guarantee system reliability. Different coding techniques have been proposed to provide the required redundancy more efficiently than…
Reed-Solomon (RS) codes are an important class of non-binary error-correction codes. They are particularly competent in correcting burst errors, being widely applied in modern communications and data storage systems. This also thanks to…
Perfect error correcting codes allow for an optimal transmission of information while guaranteeing error correction. For this reason, proving their existence has been a classical problem in both pure mathematics and information theory.…
Private information retrieval (PIR) codes and batch codes are two important types of codes that are designed for coded distributed storage systems and private information retrieval protocols. These codes have been the focus of much…
Locally repairable codes are widely applicable in contemporary large-scale distributed cloud storage systems and various other areas. By making use of some algebraic structures of elliptic curves, Li et al. developed a series of $q$-ary…
Locally repairable codes (LRCs), which can recover any symbol of a codeword by reading only a small number of other symbols, have been widely used in real-world distributed storage systems, such as Microsoft Azure Storage and Ceph Storage…
This paper presents a new construction of error correcting codes which achieves optimal recovery of a streaming source over a packet erasure channel. The channel model considered is the sliding window erasure model, with burst and arbitrary…
A code is said to be two-weight if the non-zero codewords have only two different a weight w1 and w2. Two-weight codes are closely related to strongly regular graphs. In this paper. It is shown that a consta-cyclic code of composite length…
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…
It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies…
We consider the problem of reliable communication over non-binary insertion/deletion channels where symbols are randomly deleted from or inserted in the transmitted sequence and all symbols are corrupted by additive white Gaussian noise. To…