Classification of Some Optimal Ternary Linear Codes of Small Length

Designs, Codes, and Cryptography

Volumn 10, Issue 1, 1997, Pages 63-84

  Van Eupen, Marijn ^a   Lisonẽk, Petr ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Finite geometry; Finite group action; Optimal codes; Ternary linear codes

Indexed keywords

EID: 0002225698     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008292320488     Document Type: Article

References (23)

1. S. Ball and A. Blokhuis, On the size of a double blocking set in PG(2, q), preprint.
2. R. C. Bose, Mathematical theory of the symmetrical factorial design, Sankhyā Ser. A, Vol. 8 (1947) pp. 107-166.
3. W. Bosma, J. J. Cannon and G. Mathews, Programming with algebraic structures: Design of the Magma language, In: M. Giesbrecht (ed), Proceedings of the 1994 International Symposium on Symbolic and Algebraic Computation, Oxford, July 20-22, 1994. Association for Computing Machinery, 1994, 52-57.
4. A. E. Brouwer and A. Schrijver, The blocking number of an affine space. J. Combin. Theory Ser. A, Vol. 24 (1978) pp. 251-253.
5. A. Bruen, Blocking sets in finite projective planes, SIAM J. Appl. Math., Vol. 21, No. 3 (1971) pp. 380-392.
6. C. J. Colbourn and R. C. Read, Orderly algorithms for generating restricted classes of graphs, J. Graph Th. Vol. 3 (1979) pp. 187-195.
7. M. van Eupen, Four non-existence results for ternary linear codes, to appear in IEEE Trans. Inf. Th..
8. M. van Eupen and R. Hill, An optimal ternary [69, 5, 45] code and related codes, Designs, Codes & Cryptography Vol. 4 (1994) pp. 271-282.
9. J. H. Griesmer, A bound for error-correcting codes, I.B.M. J. Res. Develop Vol. 4 (1960) pp. 532-542.
10. R. Grund, Symmetrieklassen von Abbildungen und die Konstruktion von diskreten Strukturen, Bayreuther Mathemansche Schriften Vol. 31 (1992) pp. 19-54.
11. N. Hamada, Characterization of {(q | 1) | 2, 1; t, q} min·hypers and {2(q + 1) + 2, 2; 2, q}-min·hypers in a finite projective geometry, Graphs and Combinatorics Vol. 5 (1989) pp. 63-81.
12. N, Hamada, A survey of recent work on characterization of minihypers in PG(t, q) and nonbinary linear codes meeting the Griesmer bound, J. Combin. Inform. Syst. Sci. Vol. 18 (1993) pp. 161-191.
13. 2 = 0, to appear in J. Statist. Plann. Inference.
14. N. Hamada, T. Helleseth and Ø. Ytrehus, There are exactly two nonequivalent [20, 5, 12; 3]-codes, Ars Comb Vol. 35 (1993) pp. 3-14.
15. F. Harary and E. Palmer, Graphical Enumeration, Academic Press, New York (1973).
16. R. Hill, Caps and codes, Discr. Math. Vol. 22 (1978) pp. 111-137.
17. R. Hill and D. E. Newton, Some optimal ternary linear codes, Ars Comb. Vol. 25-A (1988) pp. 61-72.
18. K. Hill and D. E. Newton, Optimal ternary codes, Designs, Codes & Cryptography Vol. 2 (1992) pp. 137-157.
19. J. W. P. Hirschfeld, Projective Geometries over Finite Fields, Oxford University Press, Oxford (1979).
20. A. Kerber, Algebraic Combinatorics via Finite Group Actions, BI Wissenschaftsverlag, Mannheim (1991).
21. V. Krishnamurthy, Combinatorics: Theory and Applications, Ellis Horwood Ltd., Chichester (1986).
22. R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and its Applications, Vol. 20, Addison-Wesley, Reading, Massachusetts (1983).
23. R. C. Read, Every one a winner, Ann. Discr. Math. Vol. 2 (1978) pp. 107-120.