Hermitian codes from higher degree places

Matthews and Michel investigated the minimum distances in certain algebraic-geometry codes arising from a higher degree place $P$. In terms of the Weierstrass gap sequence at $P$, they proved a bound that gives an improvement on the designed minimum distance. In this paper, we consider those of such codes which are constructed from the Hermitian function field. We determine the Weierstrass gap sequence $G(P)$ where $P$ is a degree 3 place, and compute the Matthews and Michel bound with the corresponding improvement. We show more improvements using a different approach based on geometry. We also compare our results with the true values of the minimum distances of Hermitian 1-point codes, as well as with estimates due Xing and Chen

A two-component model for fitting light-curves of core-collapse supernovae

We present an improved version of a light curve model, which is able to estimate the physical properties of different types of core-collapse supernovae having double-peaked light curves, in a quick and efficient way. The model is based on a two-component configuration consisting of a dense, inner region and an extended, low-mass envelope. Using this configuration, we estimate the initial parameters of the progenitor via fitting the shape of the quasi-bolometric light curves of 10 SNe, including Type IIP and IIb events, with model light curves. In each case we compare the fitting results with available hydrodynamic calculations, and also match the derived expansion velocities with the observed ones. Furthermore, we also compare our calculations with hydrodynamic models derived by the SNEC code, and examine the uncertainties of the estimated physical parameters caused by the assumption of constant opacity and the inaccurate knowledge of the moment of explosion

Light dual multinets of order six in the projective plane

The aim of this paper is twofold: First we classify all abstract light dual multinets of order $6$ which have a unique line of length at least two. Then we classify the weak projective embeddings of these objects in projective planes over fields of characteristic zero. For the latter we present a computational algebraic method for the study of weak projective embeddings of finite point-line incidence structures

Group-labeled light dual multinets in the projective plane (with Appendix)

In this paper we investigate light dual multinets labeled by a finite group in the projective plane $PG(2,\mathbb{K})$ defined over a field $\mathbb{K}$. We present two classes of new examples. Moreover, under some conditions on the characteristic $\mathbb{K}$, we classify group-labeled light dual multinets with lines of length least $9$