Acute Semigroups, the Order Bound on the Minimum Distance, and the Feng–Rao Improvements
Acute Semigroups, the Order Bound on the Minimum Distance, and the Feng–Rao Improvements
We introduce a new class of numerical semigroups, which we call the class of {\it acute} semigroups and we prove that they generalize symmetric and pseudo-symmetric numerical semigroups, Arf numerical semigroups and the semigroups generated by an interval. For a numerical semigroup $\Lambda=\{\lambda_0<\lambda_1<\dots\}$ denote $\nu_i=\#\{j\mid\lambda_i-\lambda_j\in\Lambda\}$. Given an acute numerical semigroup …