On a conjectured ideal autocorrelation sequence and a related triple-error correcting cyclic code

IEEE Transactions on Information Theory

Volumn 46, Issue 2, 2000, Pages 680-687

  Chang, Anchung ^a,b   Gaal, Peter ^c   Golomb, Solomon W ^a,d   Gong, Guang ^e   Helleseth, Tor ^a,f   Kumar, P Vijay ^a,d  

^a IEEE

^b BOEING COMPANY   (United States)

^c QUALCOMM INC   (United States)

^d UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^e UNIVERSITY OF WATERLOO   (Canada)

^f UNIVERSITY OF BERGEN   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR CORRECTION; POLYNOMIALS;

BOSE-CHAUDHURI-HOCQUENGHEM (BCH) CODE; IDEAL AUTOCORRELATION SEQUENCE; TRIPLE-ERROR CORRECTING CODES;

CODES (SYMBOLS);

EID: 0033893961     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.825842     Document Type: Article

References (20)

1. S. Boztaş and P. V. Kumar, "Binary sequences with Gold-like correlation but larger linear span," IEEE Trans. Inform. Theory, vol. 40, pp. 532-537, Mar. 1994.
2. A. Canteaut, P. Charpin, and H. Dobbertin, "Binary m-sequences with three-valued crosscorrelation: A proof of Welch's conjecture," IEEE Trans. Inform. Theory, vol. 46, pp. 4-8, Jan 2000.
3. A. Chang, "Minimum distance and decoding algorithm for cyclic codes," Ph.D. dissertation, Univ. So. Calif., Los Angeles, CA, 1998.
4. A. Chang, P. Gaal, S. W. Golomb, G. Gong, and P. V. Kumar, "On a sequence conjectured to have ideal 2-level autocorrelation function," in IEEE Int. Symp. Information Theory, Cambridge, MA, Aug. 16-21, 1998, p. 468.
5. A. Chang, T. Helleseth, and P. V. Kumar, "Further results on a conjectured 2-level autocorrelation sequence," in 36th Ann. Allerton Conf. Communication, Control and Computing, Allerton, IL, Sept. 23-25, 1998.
6. J. Dillon and H. Dobbertin, Cyclic difference sets with Singer parameters, to be published.
7. H. Dobbertin, "Kasami power functions, permutation polynomials and cyclic difference sets," in NATO-A.S.I. Workshop, Bad Windsheim, Germany, Aug. 3-14, 1998.
8. R. Gold, "Maximal recursive sequences with 3-valued recursive cross-correlation functions," IEEE Trans. Inform. Theory, vol. IT-14, pp. 154-156, Jan. 1968.
9. G. Gong and S. W. Golomb, "Hadamard transforms of three-term sequences," IEEE Trans. Inform. Theory, vol. 45, pp. 2059-2060, Sept. 1999.
10. C. R. P. Hartmann and K. K. Tzeng, "Generalization of the BCH bound," Inform. Contr., vol. 20, pp. 489-498, 1972.
11. T. Helleseth and P. V. Kumar, "Pseudonoise sequences," in The Mobile Communications Handbook, J. Gibson, Ed. New York: CRC Press and IEEE Press, 1996.
12. _, "Sequences with low correlation," in Handbook of Coding Theory, V. Pless and C. Huffman, Eds. Amsterdam, The Netherlands: Elsevier, 1998.
13. T. Kasami, "Weight distributions of Bose-Choudhary-Hochquengham codes," in Combinatorial Mathematics and its Applications. Chapel Hill, NC: Univ. North Carolina Press, 1969.
14. P. V. Kumar and C.-M. Liu, "On lower bounds to the maximum correlation of complex roots-of-unity sequences," IEEE Trans. Inform. Theory, vol. 36, pp. 633-640, May 1990.
15. F. J. Mac Williams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North Holland, 1979.
16. B. R. McDonald, Finite Rings with Identity. New York: Marcel Dekker, 1974.
17. R. J. McEliece, "On periodic sequences from GF(q)," J. Combin. Theory, vol. 10, no. 1, pp. 80-91, Jan. 1971.
18. n -1 with ideal autocorrelation," IEEE Trans. Inform. Theory, vol. 44, pp. 814-817, Mar. 1998.
19. D. V. Sarwate and M. B. Pursley, "Crosscorrelation properties of pseudorandom and related sequences," Proc. IEEE, vol. 68, pp. 593-619, 1980.
20. T. Schaub, "A linear complexity approach to cyclic codes," Ph.D. dissertation, Swiss Federal Ins. Technol., Zurich, Switzerland, 1988.