Generalized H-codes and type II codes over GF(4)

The type II codes have been studied widely in applications since their appearance. With analysis of the algebraic structure of finite field of order 4 (i.e., GF(4)), some necessary and sufficient conditions that a generalized H-code (i.e., GH-code) is a type II code over GF(4) are given in this article, and an efficient and simple method to generate type II codes from GH-codes over GF(4) is shown. The conclusions further extend the coding theory of type II.