This document describes a Fully-Specified Forward Error Correction (FEC) Scheme for the Reed-Solomon FEC codes over GF(2^^m), where m is in {2..16}, and its application to the reliable delivery of data objects on the packet erasure channel (i.e., a communication path where packets are either received without any corruption or discarded during transmission). This document also describes a Fully-...

In this correspondence, Sudan’s algorithm is modified into an efficient method to list-decode a class of codes which can be seen as a generalization of Reed–Solomon codes. The algorithm is specialized into a very efficient method for unique decoding. The code construction can be generalized based on algebraic-geometry codes and the decoding algorithms are generalized accordingly. Comparisons wi...

The compound and integrated parallel Reed-Solomon (RS) codes for multichannel communication systems are suggested. The matrix model of errors for such codes is investigated. Methods of coding and decoding of parallel RS codes, and also methods of increase of their error correcting capability are developed.

To reduce storage overhead, cloud file systems are transitioning from replication to erasure codes. This process has revealed new dimensions on which to evaluate the performance of different coding schemes: the amount of data used in recovery and when performing degraded reads. We present an algorithm that finds the optimal number of codeword symbols needed for recovery for any XOR-based erasur...

Error detection and correction plays a very important role in data communication. Various codes such as convolutional and block codes are available for the purpose of error detection and correction. Among the block codes Reed-Solomon code provides several advantages. Reed-Solomon codes are powerful error-correcting codes that finds wide applications in many fields. The soft-decision decoding of...

A list decoding for an error-correcting code is a decoding algorithm that generates a list of codewords within a Hamming distance from the received vector, where can be greater than the error-correction bound. In [18], a list-decoding procedure for Reed–Solomon codes [19] was generalized to algebraic–geometric codes. A recent work [8] gives improved list decodings for Reed–Solomon codes and alg...

Reed-Solomon codes are a class of non-binary cyclic codes which have strong burst and erasure error correction capabilities. Their current uses include deep-space communications, compact disc recordings, cellular communications, and digital broadcast[1]. Their popularity stems in part from the existence of encoding and decoding algorithms that are simple to implement in hardware. In addition to...

We give a description of the duals linearized Reed–Solomon codes in terms obtained by taking residues Ore rational functions. Our construction shows particular that, under some assumptions on base field, class is stable duality. As byproduct our work, we develop theory setting, extending results [7].

The problem of repairing linear codes and, in particular, Reed Solomon (RS) has attracted a lot attention recent years due to their extreme importance distributed storage systems. In this problem, failed code symbol (node) needs be repaired by downloading as little information possible from subset the remaining nodes. By now, there are examples RS that have efficient repair schemes, and some ev...