Computing coset leaders and leader codewords of binary codes

In this paper we use the Gr\"obner representation of a binary linear code $\mathcal C$ to give efficient algorithms for computing the whole set of coset leaders, denoted by $\mathrm{CL}(\mathcal C)$ and the set of leader codewords, denoted by $\mathrm L(\mathcal C)$. The first algorithm could be adapted to provide not only the Newton and the covering radius of $\mathcal C$ but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradient-like decoding algorithm. Another contribution of this article is the relation stablished between zero neighbours and leader codewords

Two loops calculation in chiral perturbation theory and the unitarization program of current algebra

In this paper we compare two loop Chiral Perturbation Theory (ChPT) calculation of pion-pion scattering with the unitarity second order correction to the current algebra soft-pion theorem. It is shown that both methods lead to the same analytic structure for the scattering amplitude.Comment: 13 pages, Revtex 3.0, no figures, submitted to Phys. Lett.

The 1980, 1997 and 1998 Azores earthquakes and its seismotectonic implications

We have studied the focal mechanisms of the 1980, 1997 and 1998 earthquakes in the Azores region from body-wave inversion of digital GDSN (Global Digital Seismograph Network) and broadband data. For the 1980 and 1998 shocks, we have obtained strike– slip faulting, with the rupture process made up of two sub-events in both shocks, with total scalar seismic moments of 1.9 × 1019 Nm (Mw = 6.8) and 1.4 × 1018 Nm (Mw = 6.0), respectively. For the 1997 shock, we have obtained a normal faulting mechanism, with the rupture process made up of three sub-events, with a total scalar seismic moment of 7.7 × 1017 Nm (Mw = 5.9). A common characteristic of these three earthquakes was the shallow focal depth, less than 10 km, in agreement with the oceanic-type crust. From the directivity function of Rayleigh (LR) waves, we have identified the NW–SE plane as the rupture plane for the 1980 and 1998 earthquakes with the rupture propagating to the SE. Slow rupture velocity, about of 1.5 km/s, has been estimated from directivity function for the 1980 and 1998 earthquakes. From spectral analysis and body-wave inversion, fault dimensions, stress drop and average slip have been estimated. Focal mechanisms of the three earthquakes we have studied, together with focal mechanisms obtained by other authors, have been used in order to obtain a seismotectonic model for the Azores region. We have found different types of behaviour present along the region. It can be divided into two zones: Zone I, from 30°W to 27°W; Zone II, from 27°W to 23°W, with a change in the seismicity and stress direction from Zone I. In Zone I, the total seismic moment tensor obtained corresponded to left-lateral strike–slip faulting with horizontal pressure and tension axes in the E–W and N–S directions, respectively. In Zone II, the total seismic moment tensor corresponded to normal faulting, with a horizontal tension axis trending NE–SW, normal to the Terceira Ridge. The stress pattern for the whole region corresponds to horizontal extension with an average seismic slip rate of 4.4 mm/yr

Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive

Phase space can be constructed for $N$ equal and distinguishable subsystems that could be (probabilistically) either {\it weakly} (or {\it "locally"}) correlated (e.g., independent, i.e., uncorrelated), or {\it strongly} (or {\it globally}) correlated. If they are locally correlated, we expect the Boltzmann-Gibbs entropy $S_{BG} \equiv -k \sum_i p_i \ln p_i$ to be {\it extensive}, i.e., $S_{BG}(N)\propto N$ for $N \to\infty$. In particular, if they are independent, $S_{BG}$ is {\it strictly additive}, i.e., $S_{BG}(N)=N S_{BG}(1), \forall N$. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy $S_q\equiv k [1- \sum_i p_i^q]/(q-1)$ (with $S_1=S_{BG}$) for some special value of $q\ne1$ to be the one which extensive (i.e., $S_q(N)\propto N$ for $N \to\infty$).Comment: 15 pages, including 9 figures and 8 Tables. The new version is considerably enlarged with regard to the previous ones. New examples and new references have been include