Codetables

Code Tables

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Linear Block Codes

Bounds on the minimum distance of linear block codes over GF(q) with q≤9
for given length and dimension including information on the construction.

query form

Quantum Error-Correcting Codes

2024-05-24: extended version:

qubit codes up to length 256
codes [[n,k,d]]_q for q=3,4,5,7,8 up to length 100

mainly based on

Martianus Frederic Ezerman, Markus Grassl, San Ling, Ferruh Özbudak, and Buket Özkaya.
"Characterization of Nearly Self-Orthogonal Quasi-Twisted Codes and Related Quantum Codes."
arXiv:2405.15057 [quant-ph], 2024-05-23.

and the quantum twisted codes by Bierbrauer and Edel

query form
extended version of Table III from
A. R. Calderbank, E. M. Rains, P. M. Shor and N. J. A. Sloane.
"Quantum error correction via codes over GF(4),*quot;
IEEE Transactions on Information Theory, vol. 44, no. 4, pp. 1369-1387, July 1998.
doi: 10.1109/18.681315
arXiv:quant-ph/9608006

Entanglement-Assisted Quantum Error-Correcting Codes

Bounds on the minimum distance of entanglement-assisted quantum codes for qubits and qutrits

qubit codes
qutrit codes

External Links

The MAGMA computational algebra system

codes over finite fields

Brouwer's tables (discontinued)
Chen's tables of binary quasi-cyclic codes
Chen's tables of two-weight codes
tables of Gaborit and Otmani of self-dual codes
database of self-dual codes by Masaaki Harada and Akihiro Munemasa
Houghten's tables of edit-metric codes
Houghten's tables of insertion-deletion correcting codes
MacKay's Encyclopedia of Sparse Graph Codes
Maruta's tables with bounds on n_q(k,d) for codes of small dimension
MinT, online database for optimal parameters of (t, m, s)-nets, (t, s)-sequences, orthogonal arrays, linear codes, and OOAs,
maintained by Rudolf Schürer and Wolfgang Schmid

quantum codes

table of quantum codes by Aydin
quantum twisted codes by Bierbrauer and Edel
Danielsen's database of self-dual quantum codes
table of AME states by Huber and Wyderka

curves

manYPoints, tables of curves with many rational points,
maintained by Gerard van der Geer, Everett Howe, Kristin Lauter, and Christophe Ritzenthaler

nonlinear codes

Brouwer's tables on nonlinear binary codes
tables of nonlinear binary block codes by Litsyn, Rains, and Sloane

codes over rings

table of Z₄ codes by Aydin

other sites

error correcting zoo

Acknowledgments

Thanks to everybody who has contributed to these tables (see also here).

Contact

If you have found any new codes, please send them by e-mail to

codes [at] codetables.de