Some Results on the Minimum Distance Structure of Cyclic Codes

IEEE Transactions on Information Theory

Volumn 18, Issue 3, 1972, Pages 402-409

  Hartmann, Carlos R P ^a   Tzeng, Kenneth K ^b   Chien, Robert T ^c  

^a SYRACUSE UNIVERSITY   (United States)

^b LEHIGH UNIVERSITY   (United States)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CODES, SYMBOLIC-ERROR DETECTION CAPABILITY; MATHEMATICAL TECHNIQUES-POLYNOMIALS;

CYCLIC CODES;

CODES, SYMBOLIC;

EID: 0015346031     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1972.1054816     Document Type: Article

References (18)

1. R. T. Chien and C. R. P. Hartmann, “On the minimum distance structure of cyclic codes,” presented at the IEEE Int. Symp. Information Theory, Noordwijk, Holland, June 1970.
2. R. C. Bose and D. K. Ray-Chaudhuri, “On a class of error-correcting binary group codes,” Inform. Contr., vol. 3, pp. 68–79, Mar. 1960.
3. R. C. Bose and D. K. Ray-Chaudhuri, “Further results on error-correcting binary group codes,” Inform. Contr., vol. 3, pp. 279–290, Sept. 1960.
4. A. Hocquenghem, “Codes correcteurs d'erreurs,” Chiffres, vol. 2, pp. 147–156, 1959.
5. H. F. Mattson and G. Solomon, “A new treatment of Bose-Chaudhuri codes,” SIAM, vol. 9, pp. 654–699, Dec. 1961.
6. J. MacWilliams, “A theorem on the distribution of weights in a systematic code,” Bell Syst, Tech. J., vol, 42, pp. 79–94, Jan. 1963.
7. J.-M. Goethals, “Analysis of weight distribution in binary cyclic codes,” IEEE Trans. Inform. Theory (Corresp.), vol. IT-12, pp. 401–402, July 1966.
8. —, “Factorization of cyclic codes,” IEEE Trans. Inform. Theory, vol. IT-13, pp. 242–246, Apr. 1967.
9. T. Kasami, “Some lower bounds on the minimum weight of cyclic codes of composite length,” IEEE Trans. Inform. Theory, vol. IT-14, pp. 814–818, Nov. 1968.
10. V. Lum and R. T. Chien, “On the minimum distance of Bose-Chaudhuri-Hocquenghem codes,” SIAM, vol. 16, pp. 1325–1337, Nov. 1968.
11. T. Kasami and N. Tokura, “Some remarks on BCH bounds and minimum weights of binary primitive BCH codes,” IEEE Trans. Inform. Theory, vol. IT-IS, pp. 408–413, May 1969.
12. P. Delsarte, “BCH bounds for a class of cyclic codes,” MBLE Res. Lab., Brussels, Belgium, Rep. RJ08, May 1969.
13. W. W. Peterson, Error Correcting Codes. Cambridge, Mass: M.I.T. Press and New York: Wiley, 1961.
14. V. Lum, “Comments on The weight structure of some Bose-Chaudhuri codes,” IEEE Trans. Inform. Theory (Corresp.), vol. IT-IS, pp. 618–619, Sept. 1969.
15. D. Gorenstein and N. Zierler, “A class of cyclic linear error-correcting codes in p M symbols,” SIAM J. Appl. Math., vol. 9, pp. 207–214, June 1961.
16. W. W. Peterson, “On the weight structure and symmetry of BCH _ codes,” Univ. Hawaii, Honolulu, Sci. Rep. 1, July 1965.
17. E. R. Berlekamp, Algebraic Coding Theory. New York: McGraw-Hill, 1968.
18. K. K. Tzeng and C. R. P. Hartmann, “On the minimum distance of certain reversible cyclic codes,” IEEE Trans. Inform. Theory (Corresp.), vol. IT-16. pp. 644–645. Sept. 1970.