The Nonexistence of Ternary [38, 6, 23] Codes

Designs, Codes, and Cryptography

Volumn 13, Issue 2, 1998, Pages 165-172

  Hamada, Noboru ^a   Van Eupen, Marijn ^b  

^a Osaka Prefecture University   (Japan)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Finite projective geometries; Ternary linear codes

Indexed keywords

EID: 0347015329     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008278312966     Document Type: Article

References (18)

1. G. T. Bogdanova and I. G. Boukliev, New linear codes of dimension 5 over G F(3), Proceedings of the Fourth International Workshop on Algebraic and Combinatorial Coding Theory, Novgorod, Russia, September (1994) pp. 41-43.
2. A. E. Brouwer and N. J. A. Sloane, Tables of Codes, in R. Brualdi, W. C. Huffman and V. Pless (eds.), Handbook of Coding Theory, North-Holland, Amsterdam, to appear.
3. M. van Eupen, Four nonexistence results for ternary linear codes, IEEE Trans. Inform. Theory, Vol. 41 (1995) pp. 800-805.
4. M. van Eupen, Some new results for ternary linear codes of dimension 5 and 6, IEEE Trans. Inform. Theory, Vol. 41 (1995) pp. 2048-2051.
5. M. van Eupen, N. Hamada and Y. Watamori, The nonexistence of ternary [50, 5, 32] codes, Designs, Codes and Cryptography, Vol. 7 (1996) pp. 235-237.
6. M. van Eupen and R. Hill, An optimal ternary [69, 5, 45] code and related codes, Designs, Codes and Cryptography, Vol. 4 (1994) pp. 271-282.
7. M. van Eupen and P. Lisoněk, Classification of some optimal ternary linear codes of small length, Designs, Codes and Cryptography, Vol. 10 (1997) pp. 63-84.
8. N. Hamada, A characterization of some [n, k, d; q]-codes meeting the Griesmer bound using a minihyper in a finite projective geometry, Discrete Math., Vol. 116 (1993) pp. 229-268.
9. N. Hamada, A survey of recent work on characterization of minihypers in P G(t, q) and nonbinary linear codes meeting the Griesmer bound, J. Combin. Inform. Syst. Sci., Vol. 18 (1993) pp. 161-191.
10. N. Hamada, The nonexistence of ternary [29, 6, 17] codes, Math. Japonica, Vol. 46 (1997) pp. 253-264.
11. N. Hamada and T. Helleseth, A characterization of some ternary codes meeting the Griesmer bound, Amer. Math. Soc. Contemp. Math., Vol. 168 (1994) pp. 139-150.
12. 2 - 2q; q] codes meeting the Griesmer bound, Designs, Codes and Cryptography, Vol. 2 (1992) pp. 225-229.
13. N. Hamada, T. Helleseth and φ. Ytrehus, The nonexistence of [51, 5, 33; 3] codes, Ars Combin., Vol. 35 (1993) pp. 25-32.
14. 3(6, d), 1 ≤ d ≤ 243, Math. Japonica, Vol. 43 (1996) pp. 577-593.
15. N. Hamada and Y. Watamori, The nonexistence of [71, 5, 46; 3] codes, J. Statist. Plann. Inference, Vol. 52 (1996) pp. 379-394.
16. R. Hill and D. E. Newton, Optimal ternary linear codes, Designs, Codes and Cryptography, Vol. 2 (1992) pp. 137-157.
17. I. N. Landgev, The nonexistence of some optimal ternary codes of dimension five, to appear in Designs, Codes and Cryptography.
18. R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and its Applications, Vol. 20, Addison-Wesley Publishing Company, Massachusetts (1983).