Double-circulant and bordered-double-circulant constructions for self-dual codes over $R_2$

Abstract

In this work, the double-circulant, bordered-double-circulant and stripped bordered-double-circulant constructionsfor self-dual codes over the non-chain ring $R_2 = \mathbb F_2+u\mathbb F_2+v\mathbb F_2+uv\mathbb F_2$ are introduced. Using these methods, we have constructed three extremal binary Type I codes of length $64$ of new weight enumerators for which extremal codes were not known to exist. We also give a double-circulant construction for extremal binary self-dual codes of length $40$ with covering radius $7$.