Related papers: Machine learning discovers new champion codes
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory…
We exhibit seven linear codes exceeding the current best known minimum distance d for their dimension k and block length n. Each code is defined over F_8, and their invariants [n,k,d] are given by [49,13,27], [49,14,26], [49,16,24],…
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum…
This paper introduces a new counting code. Its design was motivated by distributed video coding where, for decoding, error correction methods are applied to improve predictions. Those error corrections sometimes fail which results in…
We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic geometry codes, the algorithm is a reformulation of the…
In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed due to few slow or faulty processors). We propose a coded…
The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic…
Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…
A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name of quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the…
A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-check matrix, dimension and an upper bound on its minimum distance are obtained from the eigenstructure of the Fourier number theoretic transform.…
In this letter we consider the ensemble of codes formed by the serial concatenation of a Hamming code and two accumulate codes. We show that this ensemble is asymptotically good, in the sense that most codes in the ensemble have minimum…
Sum-rank Hamming codes are introduced in this work. They are essentially defined as the longest codes (thus of highest information rate) with minimum sum-rank distance at least $ 3 $ (thus one-error-correcting) for a fixed redundancy $ r $,…
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…
Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous theoretical and practical applications. An important goal is to obtain the best possible tradeoffs…
We prove the following results concerning the list decoding of error-correcting codes: (i) We show that for \textit{any} code with a relative distance of $\delta$ (over a large enough alphabet), the following result holds for \textit{random…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The…
Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from…