Long binary narrow-sense BCH codes are normal

Applicable Algebra in Engineering, Communications and Computing

Volumn 8, Issue 1, 1997, Pages 49-55

  Honkala, Iiro ^a   Kaipainen, Yrjö ^a   Tietäväinen, Aimo ^a  

^a UNIVERSITY OF TURKU   (Finland)

Author keywords

BCH code; Character sum; Code; Covering radius; Finite fields

Indexed keywords

LINEAR ALGEBRA; NUMBER THEORY; SET THEORY; THEOREM PROVING;

COVERING RADIUS; FINITE FIELDS; HAMMING DISTANCE; WEIL THEOREM;

BINARY CODES;

EID: 0030834731     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002000050052     Document Type: Article

References (23)

1. Calderbank, A. R.: Covering bounds for codes. J. Comb. Theory A60 117-122 (1992)
2. Calderbank, A. R.: Covering machines. Discrete Mathematics 106/107 105-110 (1992)
3. Cohen, G. D., Lobstein, A. C., Sloane, N. J. A.: Further results on the covering radius of codes. IEEE Trans. Inform. Theory 32, 680-694 (1986)
4. Deligne, P.: La conjecture de Weil. I. Inst. Hautes Etudes Sc. Publ. Math. 43, 273-307 (1974)
5. Graham, R. L., Sloane, N. J. A.: On the covering radius of codes. IEEE Trans. Inform. Theory 31, 385-401 (1985)
6. Helleseth, T.: On the covering radius of cyclic linear codes and arithmetic codes. Discrete Appl. Math. 11, 157-173 (1985)
7. Honkala, I.: Bounds for binary constant weight and covering codes. Licentiate Thesis, University of Turku, Finland, March 1987
8. Honkala, I. S.: Lower bounds for binary covering codes. IEEE Trans. Inform. Theory 34, 326-329 (1988)
9. Honkala, I. S.: Modified bounds for covering codes. IEEE Trans. Inform. Theory 37, 351-365 (1991)
10. Honkala, I.: On (q, 1)-subnormal q-ary covering codes. Discr. Appl. Math. 52, 213-221 (1994)
11. Honkala, I., Tietäväinen, A.: Codes and number theory. In: Handbook of Coding Theory Brualdi, R., Huffman, C., Pless, V. (eds) in preparation
12. Kaipainen, Y.: Chow variety. Licentiate Thesis, University of Turku, 1993 (in Finnish)
13. Lang, S., Weil, A.: Number of points of varieties in finite fields. Am. J. Math. 76, 819-827 (1954)
14. Lidl, R., Niederreiter, H.: Finite fields. Reading, MA: Addison Wesley 1983
15. MacWilliams, F. J., Sloane, N. J. A.: The Theory of Error-Correcting Codes. Amsterdam: North-Holland 1977
16. Moreno, O., Moreno, C. J.: Constructive elementary approach to the covering radius of long BCH codes. Proceedings of 2nd International Workshop on Algebraic and Combinatorial Coding Theory, Leningrad, 1990, pp. 162-165
17. Schmidt, W. M.: Equations over Finite Fields: An Elementary Approach. Berlin, Heidelberg,New York Springer 1976
18. Shparlinski, I. E.: Addition to the Russian translation of the reference [6]. Kiberneticheskiy sbornik 25, 82-84 (1988)
19. Shparlinski, I. E.: Computational and algorithmic problems in finite fields. Dordrecht Boston London: Kluwer Academic 1992
20. Tietäväinen, A.: On the covering radius of long binary BCH codes. Discrete Applied Math. 16, 75-77 (1987)
21. Tietäväinen, A.: An asymptotic bound on the covering radii of binary BCH codes. IEEE Trans. Inform. Theory 36, 211-213 (1990)
22. Vladut, S. G., Skorobogatov, A. N.: On the covering radius of long BCH codes. Probl. Peredach. Inform. 25, 38-45 (1989) (in Russian).
23. Weil, A.: On some exponential sums. Proc. Natl. Ac. Sci. 34, 204-207 (1948)