Designs in Additive Codes over GF(4)

Designs, Codes, and Cryptography

Volumn 30, Issue 2, 2003, Pages 187-199

  Kim, Jon Lark ^a   Pless, Vera ^b  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

Additive code; Assmus Mattson theorem; Generalized t design

Indexed keywords

COMPUTER AIDED DESIGN; SET THEORY; THEOREM PROVING;

ADDITIVE CODES;

BINARY CODES;

EID: 0141924300     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025484821641     Document Type: Article

References (14)

1. E. F. Assmus, Jr. and H. F. Mattson, Jr., New 5-designs, J. Combin. Theory, Vol. 6 (1969) pp. 122-151.
2. C. Bachoc and P. Gaborit, On extremal additive GF(4)-codes of lengths 10 to 18, J. Théorie Nombres Bordeaux, Vol. 12 (200) pp. 225-271.
3. A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, Quantum error correction via codes over GF(4), IEEE Trans. Inform. Theory, Vol. 44 (1998) pp. 1369-1387.
4. P. Delsarte, Four fundamental parameters of a code and their combinatorial significance, Inform. and Control, Vol. 23 (1973) pp. 407-438.
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6. I. I. Dumer and V. A. Zinov'ev, Some new maximal codes over GF(4), Problems Inform. transmission, Vol. 14 (1978) pp. 174-181; translated from Problemy Peredachi Informatsii, Vol. 14 (1978) pp. 24-34 (Russian).
7. P. Gaborit, W. C. Huffman, J.-L. Kim and V. Pless, On the classification of extremal additive codes over GF(4), In Proceedings of the 37th Allerton Conference on Communication, Control, and Computing, Urbana-Champaign (1999) pp. 535-544.
8. P. Gaborit, W. C. Huffman, J.-L. Kim and V. Pless, On additive GP(4) codes, DIMACS Workshop on Codes and Association Schemes, DIMACS Series in Discrete Math. and Theoret. Computer Science, Amer. Math. Soc., Providence, RI, Vol. 56 (2001) pp. 135-149.
9. G. Höhn, Self-dual codes over the Kleinian four group, preprint (1996). An updated version in http://xxx.lanl.gov/pdf/math.co/0005266.
10. W. C. Huffman, Characterization of quaternary extremal codes of lengths 18 and 20, IEEE Trans. Inform. Theory, Vol. 43 (1997) pp. 1613-1616.
11. C. W. H. Lam and V. Pless, There is no (24,12,10) self-dual quaternary code, IEEE Trans. Inform. Theory, Vol. 36 (1990) pp. 1153-1156.
12. V. Pless, Extremal codes are homogeneous, IEEE Trans. Inform. Theory, Vol. 35 (1989) pp. 1329-1330.
13. V. S. Pless, W. C. Huffman and R. A. Brualdi, An introduction to algebraic codes, In (V. S. Pless and W. C. Huffman, eds.), Handbook of Coding Theory, Elsevier, Amsterdam (1998) pp. 3-139.
14. E. M. Rains and N. J. A. Sloane, Self-dual codes, In (V. S. Pless and W. C. Huffman, eds.), Handbook of Coding Theory, Elsevier, Amsterdam (1998) pp. 177-294.