On the Kernel of ${\mathbb{Z}}_{2^s}$-Linear Simplex and MacDonald Codes

Cristina Fernández-Córdoba, Carlos Vela, Mercè Villanueva

The ${\mathbb{Z}}_{2^s}$-additive codes are subgroups of ${\mathbb{Z}}_{2^s}^n$, and can be seen as a generalization of linear codes over ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$. A ${\mathbb{Z}}_{2^s}$-linear code is a binary code w…