Bulletin of the
Korean Mathematical Society BKMS

We present two kinds of construction methods for self-dual codes over $\mathbb F_2+u\mathbb F_2$. Specially, the second construction (respectively, the first one) preserves the types of codes, that is, the constructed codes from Type II (respectively, Type IV) is also Type II (respectively, Type IV). Every Type II (respectively, Type IV) code over $\mathbb F_2+u\mathbb F_2$ of free rank larger than three (respectively, one) can be obtained via the second construction (respectively, the first one). Using these constructions, we update the information on self-dual codes over $\mathbb F_2+u\mathbb F_2$ of length $9$ and $10$, in terms of the highest minimum (Hamming, Lee, or Euclidean) weight and the number of inequivalent codes with the highest minimum weight.

Keywords: self-dual code, building-up construction, codes over ring, $\mathbb F_2 + u\mathbb F_2$

MSC numbers: Primary 94B60