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 recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of the representation of a finite Coxeter group W on the pth graded piece of its Orlik-Solomon algebra as a sum of characters induced from linear characters of centralizers of elements of W . Our refined conjecture relates the character of W on the pth graded piece of its Orlik-Solomon algebra with the ...

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...