Keywords: BCH codes, Best codes, binary codes, Cheng-Sloane codes, codes over GF(2), GF(3), GF(4), constant weight codes, Conway-Pless codes, Golay codes, Kschischang-Pasupathy codes, Nordstrom-Robinson code, linear codes, nonlinear codes, quantum codes, quaternary codes, Reed-Muller codes, Steiner systems, ternary codes,

• A library of linear (and some nonlinear) codes over various fields.

• Maintained by N. J. A. Sloane (email address: njas@research.att.com; home page: www.research.att.com/~njas/). Comments or contributions of further codes welcomed.

• The main references include:
  • The chapter on Self-Dual Codes, by E. M. Rains and N. J. A. Sloane, (140 pages), Handbook of Coding Theory, V. S. Pless, W. C. Huffman and R. A. Brualdi (editors), Elsevier, Amsterdam, 1998 (to appear).

  • A. E. Brouwer's web site of tables of the parameters of the best linear codes known.

  • The Theory of Error-Correcting Codes, F. J. MacWilliams and N. J. A. Sloane, Elsevier/North-Holland, Amsterdam, 1977, 762 pp.; Russian translation ``Teoriya kodov, ispravlyayushchikh oshibki'' by I. I. Grushko and V. A. Zinov'ev, edited by L. A. Bassalygo, published by Svyaz, Moscow, 1979.

• At present the format of these codes varies widely! I hope to convert them to a uniform format one day.

• This page is very much unfinished! Last modified Mar 25 1998 .

• At present the table contains (or implies) the following codes:
  
  • Binary linear codes
    • [8,4,4] Hamming code

    • [16,11,4] Hamming code

    • [23,7,9] Hashim and Poz. code

    • [27,7,12] Hashim and Con. code

    • Another version of [27,7,12] Hashim and Con. code

    • The 85 doubly-even self-dual [32,16,8] binary codes of length 32.
      Based on
      J. H. Conway and V. Pless, On The Enumeration of Self-Dual Codes, J. Combinatorial Theory, Series A vol. 28 (1980), pp. 26-53,
      and
      The Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration, [note: Table A and Table D are in separate files] J. H. Conway, V. Pless and N. J. A. Sloane, J. Combinatorial Theory, Series A, 60 (1992), pp. 183-195.

    • [32,17,8] binary linear code (Cheng-Sloane)
      

  • Binary nonlinear codes
    • See also the Library of Constant Weight Codes
    • P10b.10.36.4
      
    • BEST.10.40.4
      
    • BEST.12.144.4
      
    • Nordstrom-Robinson (16,256,6) code
      

  • Ternary linear codes
    • [13,10,3] Hamming code

    • [13,3,9] dual Hamming code

    • [40,36,3] Hamming code

    • [40,4,27] dual Hamming code

  • Quaternary linear codes
    • The Hexacode, a [6,3,4] self-dual code over GF(4)

    • [8,4,4] Hamming code tensored up to GF(4)

    • [18,9,8] self-dual code over GF(4) (Cheng-Sloane)

    • Better version of [18,9,8] self-dual code over GF(4) (Cheng-Sloane)

    • [21,3,16] dual Hamming code

    • [35,12,6] cyclic code over GF(4)

    • [35,23,8] cyclic code over GF(4) (Kschischang-Pasupathy)

  • Linear codes over Z4

  • Quantum error-correcting codes