Generalized Reed-Muller codes and curves with many points

The weight hierarchy of generalized Reed-Muller codes over arbitrary finite fields was determined by Heijnen and Pellikaan. In this paper we produce curves over finite fields with many points which are closely related to this weight hierarchy.Comment: Plain Tex, 11 page

The coset weight distributions of certain BCH codes and a family of curves

We study the distribution of the number of rational points in a family of curves over a finite field of characteristic 2. This distribution determines the coset weight distribution of a certain BCH code.Comment: Plain Tex, 15 pages; some numerical data adde

Kummer Covers with Many Points

We give a method for constructing Kummer covers with many points over finite fields.Comment: Plain Tex, 13 page

On the Existence of Supersingular Curves of Given Genus

We give a method to construct explicitly a supersingular curve of given genus g in characteristic 2.Comment: 9 pages, plain TeX, UvA-report 94-1

The contributions of matter inside and outside of haloes to the matter power spectrum

Halo-based models have been successful in predicting the clustering of matter. However, the validity of the postulate that the clustering is fully determined by matter inside haloes remains largely untested, and it is not clear a priori whether non-virialised matter might contribute significantly to the non-linear clustering signal. Here, we investigate the contribution of haloes to the matter power spectrum as a function of both scale and halo mass by combining a set of cosmological N-body simulations to calculate the contributions of different spherical overdensity regions, Friends-of-Friends (FoF) groups and matter outside haloes to the power spectrum. We find that matter inside spherical overdensity regions of size R200,mean cannot account for all power for 1<k<100 h/Mpc, regardless of the minimum halo mass. At most, it accounts for 95% of the power (k>20 h/Mpc). For 2<k<10 h/Mpc, haloes with mass M200,mean<10^11 Msun/h contribute negligibly to the power spectrum, and our results appear to be converged with decreasing halo mass. When haloes are taken to be regions of size R200,crit, the amount of power unaccounted for is larger on all scales. Accounting also for matter inside FoF groups but outside R200,mean increases the contribution of halo matter on most scales probed here by 5-15%. Matter inside FoF groups with M200,mean>10^9 Msun/h accounts for essentially all power for 3<k<100 h/Mpc. We therefore expect halo models that ignore the contribution of matter outside R200,mean to overestimate the contribution of haloes of any mass to the power on small scales (k>1 h/Mpc).Comment: 13 pages, 9 figures. Replaced to match the version accepted by MNRA

A cross-correlation-based estimate of the galaxy luminosity function

We extend existing methods for using cross-correlations to derive redshift distributions for photometric galaxies, without using photometric redshifts. The model presented in this paper simultaneously yields highly accurate and unbiased redshift distributions and, for the first time, redshift-dependent luminosity functions, using only clustering information and the apparent magnitudes of the galaxies as input. In contrast to many existing techniques for recovering unbiased redshift distributions, the output of our method is not degenerate with the galaxy bias b(z), which is achieved by modelling the shape of the luminosity bias. We successfully apply our method to a mock galaxy survey and discuss improvements to be made before applying our model to real data.Comment: 14 pages, 7 figures. Replaced to match the version accepted by MNRA