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Erschienen in:
2019 | OriginalPaper | Buchkapitel
19. Reed-Solomon Codes II
verfasst von : Lindsay N. Childs
Erschienen in: Cryptology and Error Correction
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Abstract
This chapter begins by defining the discrete Fourier transform, a square matrix \(\mathcal {F}\) whose entries are roots of unity of some field, and whose inverse is easy to write down and has almost the same form as \(\mathcal {F}\). We then look at two examples of Reed-Solomon codes, based on fields with 8 and 13 elements, respectively. For each example, encoding is done by evaluating the plaintext word W(x) at a complete set of roots of unity. As a consequence, the computational effort required in decoding to solve the set of equations to recover the original word W(x) can be substantially reduced by first multiplying the matrix of coefficients by the inverse of a discrete Fourier transform.