A Cap Found by Tallini
In [1], Tallini shows that a 41-cap in the projective space PG(4, 4), and therefore a [41, 36, 4]-code over F4 exists. In [2], Edel and Bierbrauer present explicit generator matrices for two essentially different codes with the same parameters.
Codes with these parameters are optimal.
References
| [1] | G. Tallini. Calotte complete di S4,q contenenti due quadriche ellittiche quali sezioni iperpiane. Rend. Mat. e Appl., 23:108–123, 1964. |
| [2] | Yves Edel and Jürgen Bierbrauer. 41 is the largest size of a cap in PG(4, 4). Designs, Codes and Cryptography, 16(2):151–160, February 1999. doi:10.1023/A:1008389013117 |
Copyright
Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.
Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “A Cap Found by Tallini.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2024-09-05.
http://mint.sbg.ac.at/desc_CB4M5Cap.html