Norm-trace-lifted codes over binary fields

In this paper, we introduce norm-trace-lifted codes over binary fields, which are codes with locality and high availability based on the norm-trace curve over the field ${\mathbb{F}_{{2^r}}}$. While they are inspired by Hermitian-lifted codes, norm-trace-lifted codes are easier to define and provide some potential advantages in terms of locality, meaning the number of symbols required to recover another, or alphabet size.