A Library of Linear (and Nonlinear) Codes
N. J. A. Sloane
codes over GF(2), GF(3), GF(4),
constant weight codes,
A library of linear (and some nonlinear) codes over various fields.
Maintained by N. J. A. Sloane
Comments or contributions of further codes welcomed.
The main references include:
- The chapter on
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
of the parameters of the best linear codes known.
The Theory of Error-Correcting Codes,
F. J. MacWilliams and N. J. A. Sloane,
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.
J. H. Conway and V. Pless, On The Enumeration
of Self-Dual Codes, J. Combinatorial Theory, Series A vol. 28
(1980), pp. 26-53,
Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration,
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
- Ternary linear codes
- 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
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