Some new Results for Additive Self-Dual Codes over GF(4)

Varbanov, Zlatko. "Some new Results for Additive Self-Dual Codes over GF(4)." Serdica Journal of Computing 1.2 (2007): 213-227. <http://eudml.org/doc/11421>.

@article{Varbanov2007,
abstract = {* Supported by COMBSTRU Research Training Network HPRN-CT-2002-00278 and the Bulgarian National Science Foundation under Grant MM-1304/03.Additive code C over GF(4) of length n is an additive subgroup of GF(4)n. It is well known [4] 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.},
author = {Varbanov, Zlatko},
journal = {Serdica Journal of Computing},
keywords = {Additive Code; Self-Dual Code; Graph Code; Classification; additive code; self-dual code; graph code; classification},
language = {eng},
number = {2},
pages = {213-227},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Some new Results for Additive Self-Dual Codes over GF(4)},
url = {http://eudml.org/doc/11421},
volume = {1},
year = {2007},
}

TY - JOUR
AU - Varbanov, Zlatko
TI - Some new Results for Additive Self-Dual Codes over GF(4)
JO - Serdica Journal of Computing
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 1
IS - 2
SP - 213
EP - 227
AB - * Supported by COMBSTRU Research Training Network HPRN-CT-2002-00278 and the Bulgarian National Science Foundation under Grant MM-1304/03.Additive code C over GF(4) of length n is an additive subgroup of GF(4)n. It is well known [4] 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.
LA - eng
KW - Additive Code; Self-Dual Code; Graph Code; Classification; additive code; self-dual code; graph code; classification
UR - http://eudml.org/doc/11421
ER -