The Type 2 Property for Self-Dual Codes over Finite Fields of Characteristic Two
耕一 別宮 · 2001
The Type II property with respect to a trace-orthogonal basis (TOB) of F2r over F2 for self-dual codes over F2r has been introduced by Harada, Munemasa and the author, as a generalization of the doubly-even property of binary self-dual codes. In this paper, we show that the Type II property for a selfdual code over F2r is independent of the choice of a TOB of F2r over F2, by establishing some necessary and sufficient conditions for the Type II property. One involves a Galois ring. Another involves the orthogonality between a Z4code and the Z4-Kerdock code. We also show that the Type II property with respect to a non-TOB of F2r over F2 is stronger than the Type II property with respect to any TOB of F2r over F2.