In this work we investigate and compare bounds on throughput and delay performance of code-based scheduling protocols derived from the codewords of Reed-Solomon and Hermitian codes. It is found that Hermitian codes outperform Reed-Solomon codes in minimum throughput guarantee and delay metrics when the number of nodes is in the order of thousands. The relative minimum distance of a code is iden...

The best known constructions for arrays with low bias are those from [1] and the exponential sum method based on the WeilCarlitz-Uchiyama bound. They all yield essentially the same parameters. We present new efficient coding-theoretic constructions, which allow farreaching generalizations and improvements. The classical constructions can be described as making use of Reed-Solomon codes. Our rec...

We begin with the definition of Reed-Solomon codes. Definition 1.1 (Reed-Solomon code). Let Fq be a finite field and Fq[x] denote the Fq-space of univariate polynomials where all the coefficients of x are from Fq. Pick {α1, α2, ...αn} distinct elements (also called evaluation points) of Fq and choose n and k such that k ≤ n ≤ q. We define an encoding function for Reed-Solomon code as RS : Fq → ...

In the past few years, all manner of storage systems, ranging from disk array systems to distributed and widearea systems, have started to grapple with the reality of tolerating multiple simultaneous failures of storage nodes. Unlike the single failure case, which is optimally handled with RAID Level-5 parity, the multiple failure case is more difficult because optimal general purpose strategie...

Digital audio broadcasting (DAB) systems for the AM band are being developed to provide higher-quality radio broadcasts, broader coverage, and data services. Transmission is typically done by means of multistreaming with QAM/OFDM in the high bits/sec/Hz regime, in which Reed–Solomon codes, either alone or in concatenation with inner trellis coded modulation (TCM), are natural choices for error ...

In this paper, some new classes of entanglement-assisted quantum MDS codes (EAQMDS for short) are constructed via generalized Reed–Solomon over finite fields odd characteristic. Among our constructions, there many EAQMDS with lengths. The lengths these may not be divisors $$q^2\pm 1$$ , which and have never been reported.

Distributed storage systems for large clusters typically use replication to provide reliability. Recently, erasure codes have been used to reduce the large storage overhead of threereplicated systems. Reed-Solomon codes are the standard design choice and their high repair cost is often considered an unavoidable price to pay for high storage efficiency and high reliability. This paper shows how ...