Title :
On Systematic Generator Matrices for Reed–Solomon Codes
Author :
Versfeld, Daniel J J ; Ridley, James N. ; Ferreira, Hendrik C. ; Helberg, Albert S J
Author_Institution :
Sch. of Electr. & Inf. Eng., Univ. of the Witwatersrand, Johannesburg, South Africa
fDate :
6/1/2010 12:00:00 AM
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.
Keywords :
Reed-Solomon codes; decoding; error correction codes; matrix algebra; Reed-Solomon code; erasures-only decoding; systematic generator matrix; Africa; Code standards; Conferences; Decoding; Error correction codes; Honorary membership; Interpolation; Mathematics; Polynomials; Telecommunication computing; Encoding; Reed–Solomon codes; erasures-only decoding; error correction coding; generator matrix;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2046104
