On systematic generator matrices for Reed-Solomon codes

Authors:
Daniel J. J. Versfeld;James N. Ridley;Hendrik C. Ferreira;Albert S. J. Helberg
Affiliations:
School of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg, South Africa;John Knopfmacher Center, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa;Department of Electrical and Electronic Engineering, University of Johannesburg, Johannesburg, South Africa;Department of Quality and Education, Faculty of Engineering, North-West University, Potchefstroom, South Africa
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

We derive a simple formula to generate a wide-sense systematic generator matrix B for a Reed-Solomon code. Specifically, we generate the generator matrix B such that the columns with indices ρ1, ρ2,..., ρk are the columns of the identity matrix Ik. One possible application of these wide-sense matrices is erasures-only decoding.