## Erik Agrell's tables of binary block codes

### Purpose

This website forms an electronic supplement to the papers [1] and [2] by
Erik Agrell, Alexander Vardy, and
Kenneth Zeger.
It contains tables of bounds on the size of binary unrestricted codes,
constant-weight codes, doubly-bounded-weight codes, and doubly-constant-weight
codes.

The site is maintained as an online resource for the best known
*upper* bounds for these classes of binary block codes. Hence, we would
like to hear of any progress that is made, such as improved bounds or
corrections. Tables of *lower* bounds are available elsewhere; see the links below.

### Tables

- Bounds on
*A*(*n*,*d*),
the maximum size of an
(*n*,*d*)
unrestricted binary code.
- Bounds on
*A*(*n*,*d*,*w*),
the maximum size of an
(*n*,*d*,*w*)
constant-weight binary code.
- Bounds on
*T´*(*w*_{1},*n*_{1},*w*_{2},*n*_{2},*d*),
the maximum size of a
(*w*_{1},*n*_{1},*w*_{2},*n*_{2},*d*)
doubly-bounded-weight binary code.
- Bounds on
*T*(*w*_{1},*n*_{1},*w*_{2},*n*_{2},*d*),
the maximum size of a
(*w*_{1},*n*_{1},*w*_{2},*n*_{2},*d*)
doubly-constant-weight binary code.

For definitions of these four classes of binary codes and their parameters,
see [1].

Related tables of bounds for various classes of codes are maintained on the following sites.
[B]
A. E. Brouwer: Upper and lower bounds for unrestricted
binary,
ternary, and quaternary codes and for linear *q*-ary codes. The tables constitute online versions of [4] and are regularly updated (2004).

[C]
E. Z. Chen: Lower bounds for binary quasi-cyclic codes.

[J]
D. B. Jaffe: Upper and lower bounds for binary linear codes.

[LRS]
S. Litsyn, E. M. Rains, and N. J. A. Sloane: Extensive tables of lower bounds for unrestricted binary codes.
This is an online version of [6], updated until 1999. (Here is a slightly older version.)

[RS]
E. M. Rains, and N. J. A. Sloane: Lower bounds for constant-weight binary codes, with upper bounds where they are known to coincide with the lower bounds. This is an online version of [5].

### References

[1]
E. Agrell, A. Vardy, and
K. Zeger,
"Upper bounds for constant-weight codes,"
*IEEE Transactions on Information Theory*,
vol. 46, no. 7, pp. 2373-2395, Nov. 2000.

[2]
E. Agrell, A. Vardy, and
K. Zeger,
"A table of upper bounds for binary codes,"
*IEEE Transactions on Information Theory*,
vol. 47, no. 7, pp. 3004-3006, Nov. 2001.
Correction

[3] M. R. Best, A. E. Brouwer, F. J. MacWilliams, A. M. Odlyzko,
and N. J. A. Sloane,
"Bounds for binary codes of length less than 25,"
*IEEE Transactions on Information Theory*,
vol. IT-24, no. 1, pp. 81-93, January 1978.

[4] A. E. Brouwer,
"Bounds on the size of linear codes,"
in *Handbook of Coding Theory*
(V. S. Pless and W. C. Huffman, eds.),
vol. 1, pp. 295-461, Amsterdam, The Netherlands: Elsevier, 1998.

[5] A. E. Brouwer, J. B. Shearer, N. J. A. Sloane, and W. D. Smith,
"A new table of constant weight codes,"
*IEEE Transactions on Information Theory*,
vol. 36, no. 6, pp. 1334-1380, Nov. 1990.

[6] S. Litsyn,
"An updated table of the best binary codes known,"
in *Handbook of Coding Theory*
(V. S. Pless and W. C. Huffman, eds.),
vol. 1, pp. 463-498, Amsterdam, The Netherlands: Elsevier, 1998.

[7] B. Mounits, T. Etzion, and S. Litsyn,
"Improved upper bounds on sizes of codes,"
*IEEE Transactions on Information Theory*,
vol. 48, no. 4, pp. 880-886, Apr. 2002.

[8] A. Schrijver,
"New code upper bounds from the Terwilliger algebra,"
preprint, Apr. 2004.

[9] D. Smith, A. Sakhnovich, S. Perkins, D. Knight, and L. Hughes,
"Application of coding theory to the design of frequency hopping lists,"
Tech. report UG-M-02-1, Div. of Math. and Stat.,
Univ. of Glamorgan, Wales, U.K., Feb. 2002.