Related papers: Real-time error correction codes for deletable err…
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by…
In this work we present a class of locally recoverable codes, i.e. codes where an erasure at a position $P$ of a codeword may be recovered from the knowledge of the entries in the positions of a recovery set $R_P$. The codes in the class…
Erasure codes have emerged as an efficient technology for providing data redundancy in distributed storage systems. However, it is a challenging task to repair the failed storage nodes in erasure-coded storage systems, which requires large…
Reed-Muller codes encode an $m$-variate polynomial of degree $r$ by evaluating it on all points in $\{0,1\}^m$. We denote this code by $RM(m,r)$. The minimal distance of $RM(m,r)$ is $2^{m-r}$ and so it cannot correct more than half that…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
The doubly shortened perfect codes of length 13 are classified utilizing the classification of perfect codes in [P.R.J. \"Osterg{\aa}rd and O. Pottonen, The perfect binary one-error-correcting codes of length 15: Part I - Classification,…
We discuss how subspace codes can be used to simultaneously correct errors and erasures when the network performs random linear network coding and the edges are noisy channels. This is done by combining the subspace code with a classical…
We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been…
We revisit the error correction scheme of real-valued signals when the codeword is corrupted by gross errors on a fraction of entries and a small noise on all the entries. Combining the recent developments of approximate message passing and…
The locally repairable codes (LRCs) were introduced to correct erasures efficiently in distributed storage systems. LRCs are extensively studied recently. In this paper, we first deal with the open case remained in \cite{q} and derive an…
In 2007, Martinian and Trott presented codes for correcting a burst of erasures with a minimum decoding delay. Their construction employs [n,k] codes that can correct any burst of erasures (including wrap-around bursts) of length n-k. The…
Erasures are the primary type of errors in physical systems dominated by leakage errors. While quantum error correction (QEC) using stabilizer codes can combat erasure errors, it remains unknown which constructions achieve capacity…
Construction of error-correcting codes achieving a designated minimum distance parameter is a central problem in coding theory. In this work, we study a very simple construction of binary linear codes that correct a given number of errors…
In this paper, we propose a partitioning technique that decomposes a pair of sequences with overlapping $t$-deletion $s$-substitution balls into sub-pairs, where the $^{\leq}t$-burst-deletion balls of each sub-pair intersect. This…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the…
A novel adaptive binary decoding algorithm for LDPC codes is proposed, which reduces the decoding complexity while having a comparable or even better performance than corresponding non-adaptive alternatives. In each iteration the variable…
Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable…
Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…