This book is an extended and revised version of" Numerical Semigroups with Applications,"
published by Springer as part of the RSME series. Like the first edition, it presents …

We present procedures to calculate the set of Arf numerical semigroups with given genus,
given conductor and given genus and conductor. We characterize the Kunz coordinates of …

Numerical Semigroups Page 1 JC Rosales PA García-Sánchez DEVELOPMENTS IN
MATHEMATICS 20 Numerical Semigroups Page 2 NUMERICAL SEMIGROUPS Page 3 …

In this paper we elaborate on the structure of the semigroup tree and the regularities on the
number of descendants of each node observed earlier by the first author. These regularities …

We develop new coset bounds for algebraic geometric codes. The bounds have a natural
interpretation as an adversary threshold for algebraic geometric secret sharing schemes and …

The weight hierarchy of one-point algebraic geometry codes can be estimated by means of
the generalized order bounds, which are described in terms of a certain Weierstrass …

We give some general bounds and formulas for the generalized Feng–Rao distances (or
generalized order bounds) in an arbitrary numerical semigroup. The obtained results can be …

We introduce a new class of numerical semigroups, which we call the class of acute
semigroups and we prove that they generalize symmetric and pseudosymmetric numerical …

A sharp upper bound for the maximum integer not belonging to an ideal of a numerical
semigroup is given and the ideals attaining this bound are characterized. Then, the result is …

Sakata's generalization of the Berlekamp–Massey algorithm applies to a broad class of
codes defined by an evaluation map on an order domain. In order to decode up to the …