Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Journal of Computing, Vol. 1, No 2, (2007), 213p-227p
Additive code C over GF(4) of length n is an additive subgroup
of GF(4)n. It is well known  that the problem of finding stabilizer
quantum error-correcting codes is transformed into problem of finding additive
self-orthogonal codes over the Galois field GF(4) under a trace inner
product. Our purpose is to construct good additive self-dual codes of length
13 ≤ n ≤ 21. In this paper we classify all extremal (optimal) codes of
lengths 13 and 14, and we construct many extremal codes of lengths 15 and
16. Also, we construct some new extremal codes of lengths 17,18,19, and 21.
We give the current status of known extremal (optimal) additive self-dual
codes of lengths 13 to 21.
* Supported by COMBSTRU Research Training Network HPRN-CT-2002-00278 and the Bulgarian National Science Foundation under Grant MM-1304/03.