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

Abstract

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.