Algebraic decoding of (103, 52, 19) and (113, 57, 15) quadratic residue codes

IEEE Transactions on Communications

Volumn 53, Issue 5, 2005, Pages 749-754

  Truong, Trieu Kien ^a   Chang, Yaotsu ^a   Chen, Yan Haw ^a   Lee, Chong Dao ^a  

^a I SHOU UNIVERSITY   (Taiwan)

Author keywords

Inverse free Berlekamp Massey (BM) algorithm; Irreducible generator polynomial; Quadratic residue codes; Unknown syndromes

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DATA COMMUNICATION SYSTEMS; DECODING; MATRIX ALGEBRA; POLYNOMIALS;

INVERSE FREE BERLEKAMP-MASSEY (BM) ALGORITHM; IRREDUCIBLE GENERATOR POLYNOMIAL; QUADRATIC RESIDUE CODES; UNKNOWN SYNDROMES;

BINARY CODES;

EID: 20144385137     PISSN: 00906778     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCOMM.2005.847147     Document Type: Article

References (22)

1. E. Prange, "Some Cyclic Error-Correcting Codes with Simple Decoding Algorithms," Air Force Cambridge Res. Center, Cambridge, MA, TN-58-156, 1958.
2. F. J. MacWilliams and N. J. A. Sloan, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1977.
3. J. Wolfmann, "A permutation decoding of the (24, 12, 8) Golay code," IEEE Trans. Inf. Theory, vol. IT-29, no. 5, pp. 748-750, Sep. 1983.
4. T. Kasami, "A decoding procedure for multiple-error-correcting cyclic codes," IEEE Trans. Inf. Theory, vol. IT-10, no. 2, pp. 134-138, Apr. 1964.
5. M. Blaum and J. Bruck, "Decoding the Golay code with Venn diagrams," IEEE Trans. Inf. Theory, vol. 36, no. 4, pp. 906-910, Jul. 1990.
6. V. Pless, "Decoding the Golay codes," IEEE Trans. Inf. Theory, vol. IT-32, no. 4, pp. 561-567, Jul. 1986.
7. J. Yuan, C. S. Chen, and S. Ma, "Two-level decoding of (32, 16, 8) quadratic residue code," Proc. IEE Commun. Speech Vis., vol. 140, no. 6, pp. 409-414, Dec. 1993.
8. M. Elia, "Algebraic decoding of the (23,12, 7) Golay code," IEEE Trans. Inf. Theory, vol. 33, no. 1, pp. 150-151, Jan. 1987.
9. I. S. Reed, X. Yin, T. K. Truong, and J. K. Holmes, "Decoding the (24, 12, 8)Golay code," Proc. Inst. Elect. Eng., vol. 137, no. 3, pp. 202-206, May 1990.
10. I. S. Reed, X. Yin, and T. K. Truong, "Algebraic decoding of the (32, 16, 8) quadratic residue code," IEEE Trans. Inf. Theory, vol. 36, no. 4, pp. 876-880, Jul. 1990.
11. I. S. Reed, T. K. Truong, X. Chen, and X. Yin, "The algebraic decoding of the (41, 21, 9) quadratic residue code," IEEE Trans. Inf. Theory, vol. 38, no. 3, pp. 974-985, May 1992.
12. X. Chen, I. S. Reed, and T. K. Truong, "Decoding the (73, 37, 13) quadratic residue code," in Proc. IEE Comput. Digit. Tech., vol. 141, Sep. 1994, pp. 253-258.
13. Y. Chang, T. K. Truong, I. S. Reed, H. Y. Cheng, and C. D. Lee, "Algebraic decoding of the (71, 36, 11), (79, 40, 15), and (97, 49, 15) quadratic residue codes," IEEE Trans. Commun., vol. 51, no. 9, pp. 1463-1473, Sep. 2003.
14. R. He, I. S. Reed, T. K. Truong, and X. Chen, "Decoding the (47, 24, 11) quadratic residue code," IEEE Trans. Inf. Theory, vol. 47, no. 3, pp. 1181-1186, Mar. 2001.
15. E. R. Berlekamp, Algebraic Decoding Theory. New York: McGraw-Hill, 1968.
16. J. L. Massey, "Shift-register synthesis and BCH decoding," IEEE Trans. Inf. Theory, vol. IT-15, no. 1, pp. 122-127, Jan. 1969.
17. I. S. Reed, M. T. Shih, and T. K. Truong, "VLSI design of inverse-free Berlekamp-Massey algorithm," Proc. Inst. Elect. Eng., vol. 138, no. 5, pp. 295-298, Sep. 1991.
18. X. Youzhi, "Implementation of Berlekamp-Massey algorithm without inversion," in Proc. IEE Commun. Speech Vis., vol. 138, Jun. 1991, pp. 138-140.
19. M. Karlin, "New binary coding results by circulants," IEEE Trans. Inf. Theory, vol. IT-15, no. 1, pp. 81-92, Jan. 1969.
20. D. Coppersmith and G. Seroussi, "On the minimum distance of some quadratic residue codes," IEEE Trans. Inf. Theory, vol. IT-30, no. 2, pp. 407-411, Mar. 1984.
21. T. K. Truong, J. H. Jeng, and I. S. Reed, "Fast algorithm for computing the roots of the error locator polynomials up to degree 11 in Reed-Solomon decoders," IEEE Trans. Commun., vol. 49, no. 5, pp. 779-783, May 2001.
22. S. V. Fedorenko and P. V. Trifonov, "Finding roots of polynomials over finite fields," IEEE Trans. Commun., vol. 50, no. 11, pp. 1709-1711, Nov. 2002.