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There are different ways to realize Reed Solomon (RS) codes. While in the storage community, using the generator matrices to implement RS codes is more popular, in the coding theory community the generator polynomials are typically used to realize RS codes. Prominent exceptions include HDFS-RAID, which uses generator polynomial based erasure codes, and extends the Apache Hadoops file system. In this paper we evaluate the performance of an implementation of polynomial realization of Reed-Solomon codes, along with our optimized version of it, against that of a widely-used library (Jerasure) that implements the main matrix realization alternatives. Our experimental study shows that despite significant performance gains yielded by our optimizations, the polynomial implementations performance is constantly inferior to those of matrix realization alternatives in general, and that of Cauchy bit matrices in particular.
In this article we count the number of generalized Reed-Solomon (GRS) codes of dimension k and length n, including the codes coming from a non-degenerate conic plus nucleus. We compare our results with known formulae for the number of 3-dimensional MDS codes of length n=6,7,8,9.
Projective Reed-Solomon (PRS) codes are Reed-Solomon codes of the maximum possible length q+1. The classification of deep holes --received words with maximum possible error distance-- for PRS codes is an important and difficult problem. In this paper
In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless, we show th
We study the problem of classifying deep holes of Reed-Solomon codes. We show that this problem is equivalent to the problem of classifying MDS extensions of Reed-Solomon codes by one digit. This equivalence allows us to improve recent results on the
Linearized Reed-Solomon (LRS) codes are sum-rank metric codes that fulfill the Singleton bound with equality. In the two extreme cases of the sum-rank metric, they coincide with Reed-Solomon codes (Hamming metric) and Gabidulin codes (rank metric). L