Self-dual codes over GF(2), GF(3) and GF(4) were classified from the early 70’s until the early 80’s. A method for how to do this and eficient descriptions of the codes were developed [3], [4], [17], [20], [21]. New results related to the binary classifications have recently appeared. New formats and classifications have also recently occurred. These events, their relations to the old classifications and open problems will be given.


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  1. 1.
    Bachoc, C.: On harmonic weight enumerators of binary codes. DESI (1999) 11–28.Google Scholar
  2. 2.
    Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correctionvia codes over GF(4). IEEE Trans. Inform. Th. IT-44 (1998) 1369–1387.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Conway, J.H., Pless, V.: An enumeration of self-dual codes. JCT(A) 28 (1980)26–53.zbMATHMathSciNetGoogle Scholar
  4. 4.
    Conway, J.H., Pless, V., Sloane, N.J.A.: Self-dual codes over GF(3) and GF(4) oflength not exceeding 16. IEEE Trans. Inform. Th. IT-25 (1979) 312–322.CrossRefMathSciNetGoogle Scholar
  5. 5.
    Conway, J.H., Sloane, N.J.A.: A new upper bound on the minimum distance ofself-dual codes.IEEE Trans. Inform. Th. IT-36 (1990) 1319–1333.CrossRefGoogle Scholar
  6. 6.
    Conway, J.H., Sloane, N.J.A.: Self-dual codes over the integers modulo 4. JCT(A)62 (1993) 31–45.Google Scholar
  7. 7.
    Fields, J.E., Gaborit, P., Huffman, W.C., Pless, V.: All Self-Dual Z4 Codes ofLength 15 or Less are Known. IEEE Trans. Inform. Th.44 (1998) 311–322.zbMATHCrossRefGoogle Scholar
  8. 8.
    Fields, J.E., Gaborit, P., Huffman, W.C., Pless, V.: On the classification of formallyself-dual codes. Proceedings of thirty-sixth Allerton Conference, UIUC, (1998) 566–575.Google Scholar
  9. 9.
    Fields, J.E., Gaborit, P., Huffman, W.C., Pless, V.: On the classification of extremal,even formally self-dual codes. DESI 18 (1999) 125–148.zbMATHMathSciNetGoogle Scholar
  10. 10.
    Fields, J.E., Gaborit, P., Huffman, W.C., Pless, V.: On the classification of extremal,even, formally self-dual codes of lengths 20 and 22 (preprint).Google Scholar
  11. 11.
    Gaborit, P.: Mass formulas for self-dual codes over Z4 and Fq + uFq rings.IEEETrans. Inform. Th.42(1996) 1222–1228.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Gaborit, P., Huffman, W.C., Kim, J.L., Pless, V.: On Additive GF(4) Codes.DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 56(2001) 135–149.MathSciNetGoogle Scholar
  13. 13.
    Hohn, G.: Self-dual codes over Kleinian four group. (preprint) 1996.Google Scholar
  14. 14.
    Gulliver, T.A., Harada, M.: Classification of extremal double circulant formallyself-dual even codes. DESI 11 (1997) 25–35.zbMATHMathSciNetGoogle Scholar
  15. 15.
    Kennedy, G.T., Pless, V.: On designs and formally self-dual codes. DESI 4 (1994)43–55.zbMATHMathSciNetGoogle Scholar
  16. 16.
    Pless, V.: On the uniqueness of the Golay codes. JCT(A) 5 (1968) 215–228.zbMATHMathSciNetGoogle Scholar
  17. 17.
    Pless, V.: A classification of self-orthogonal codes over GF(2). Discrete Math. 3(1972) 209–246.zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Pless, V.: Introduction to the Theory of Error Correcting Codes, third edition,New York, Wiley, 1998.zbMATHGoogle Scholar
  19. 19.
    Pless, V., Leon, J.S., Fields, J.: All Z 4 Codes of Type II and Length 16 are known.JCT(A) 78 (1997) 32–50.zbMATHMathSciNetGoogle Scholar
  20. 20.
    Pless, V., Sloane, N.J.A.: On the classification and enumeration of self-dual codes.JCT(A) 18 (1975) 313–333.zbMATHMathSciNetGoogle Scholar
  21. 21.
    Pless, V., Sloane, N.J.A., Ward, H.N.: Ternary codes of minimum weight 6 and theclassification of self-dual codes of length 20. IEEE Trans. Inform. Th. 26 (1980)305–316.zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Rains, E.M.: Shadow bounds for self-dual codes. IEEE Trans. Inform. Th. 44(1998) 134–139.zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Rains, E.M., Sloane, N.J.A.: Self-dual codes. Handbook of Coding Theory.V. Plessand W.C. Huffman, North Holland, eds., Amsterdam, 1998.Google Scholar
  24. 24.
    Simonis, J.: The [18],[9],[6] code is unique. Discrete Math. 106/107 (1992) 439–448.CrossRefMathSciNetGoogle Scholar
  25. 25.
    Ward, H.N.: A bound for divisible codes. IEEE Trans. Inform. Th. 38 (1992) 191–194.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001 2001

Authors and Affiliations

  • Vera Pless
    • 1
  1. 1.Department of Mathematics Statistics,and Computer Science (MC 249)University of Illinois at ChicagoChicago

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