In the last lecture, we studied codes based on univarite polynomials, also known as Reed-Solomon codes, and on multivariate polynomials, also known as Reed-Muller codes. The Reed-Solomon codes had rate R = 1 − δ, which is optimal (given by the Singleton bound), but required alphabets of large size (|Σ| ≥ n). Multivariate polynomials in a constant number of variables, however, gave codes of posi...

SRA used a language-independent, domain-independent, multipurpose text understanding system as the core of the M UC-5 system for extraction from English and Japanese joint venture texts, SRA 's NLP core systelll, SOLOMON, has been under development since 1986. It has been used for a variety of domains, and was aimed from the start to be language-independent, domain-independent, and application-...

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...

s and Presentations:  UWC Science Research Open Day (2011): Poster Presentation Erasmus N, Solomon MC, Fortuin KA, Henkel RR: Effect of Eurycoma longifolia Jack (Tongkat Ali) extract on human spermatozoa in vitro, Bellville, South Africa; abstract book p. 33.  40 Physiology Society of Southern Africa (2012): Oral Presentation Erasmus N, Solomon MC, Fortuin KA, Henkel RR: Effect of aqueous ext...

The Orlik-Solomon algebra of a matroid M is the quotient of the exterior algebra on the points by the ideal I(M) generated by the boundaries of the circuits of the matroid. There is an isomorphism between the OrlikSolomon algebra of a complex matroid and the cohomology of the complement of a complex arrangement of hyperplanes. In this article a generalization of the Orlik-Solomon algebras, call...

Error correcting codes are used for detection and correction of errors in digital communication system. Error correcting coding is based on appending of redundancy to the information message according to a prescribed algorithm. Reed Solomon codes are part of channel coding and withstand the effect of noise, interference and fading. Galois field arithmetic is used for encoding and decoding reed ...

Let (W,S) be a finite Coxeter system. Tits defined an associative product on the set Σ of simplices of the associated Coxeter complex. The corresponding semigroup algebra is the Solomon-Tits algebra of W . It contains the Solomon algebra of W as the algebra of invariants with respect to the natural action of W on Σ. For the symmetric group Sn, there is a 1-1 correspondence between Σ and the set...

RECONSTRUCTION OF PREHISTORIC exchange systems in Island Melanesia is becoming increasingly possible as archaeological activity continues to expand our knowledge of areas formerly labeled terra incognita. The Solomon Islands represent such an area, although much of the archipelago remains little known or unknown archaeologically. The objective of this paper is to examine recent evidence for pas...