On systematic generator matrices for Reed-Solomon codes
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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 ¿ 1 , ¿ 2 ,..., ¿ k are the columns of the identity matrix Ik . One possible application of these wide-sense matrices is erasures-only decoding
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Versfeld, D.J.J. et al. 2010. On systematic generator matrices for Reed-Solomon codes. IEEE transactions on information theory, 56(6):2549-2550. [https:/doi.org/10.1109/TIT.2010.2046104]