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Fast, prime factor, discrete Fourier transform algorithms over GF(2) for 8 ? m ? 10 |
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| Authors: | TK Truong PD Chen |
| Affiliation: | a Department of Information Engineering, I-Shou University, 1, Section 1, Hsueh-Cheng Rd, Ta-Hsu Hsiang, Koahsiung County 84008, Taiwan b Department of Information Technology, National Pingtung Institute of Commerce, Pingtung 900, Taiwan c Department of Electrical Engineering-Systems, EEB 500, University of Southern California, Los Angeles, CA 90089-2565, USA |
| Abstract: | In this paper it is shown that Winograd’s algorithm for computing convolutions and a fast, prime factor, discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of 2m − 1 points over GF(2m), for 8 ? m ? 10. These new transform techniques can be used to decode Reed-Solomon (RS) codes of block length 2m − 1. The complexity of this new transform algorithm is reduced substantially from more conventional methods. A computer simulation verifies these new results. |
| Keywords: | Winograd&rsquo s algorithm Prime factor DFT algorithm Cyclic convolution Reed-Solomon codes |
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