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Abstract
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By puncturing the Reed–Solomon codes with the block lengths of 2m, it is possible to
design systematic and nonsystematic codes with arbitrary block lengths and rates that can
be decoded using FFT. Because the Reed–Solomon (RS) codes are maximum distance separable
(MDS), the resultant codes keep this property as well. The codes are constructed over prime fields
as opposed to the conventional practice of extension fields, and hence additions and multiplications
are simple mod operations and there is no need to use polynomials and look-up tables
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