Computer search for curves with many points among certain quotient curves of the Fermat curves

We make computer search among curves defined by ya = xb (1 - xc)d over Fpn where p does notdivide a and c, one of gcd(a, b + cd), gcd(a,d) and gcd(a, b) is 1. As the result we find new curveswith many rational points, where we can update many entries of manypoints.org

New sextics of genus 6 and 10 attaining the Serre bound

We provide new examples of curves of genus 6 or 10 attaining the Serre bound. They all belong to the family of sextics introduced in [19] as a a generalization of the Wiman sextics [36] and Edge sextics [9]. Our approach is based on a theorem by Kani and Rosen which allows, under certain assumptions, to fully decompose the Jacobian of the curve. With our investigation we are able to update several entries in \url{http://www.manypoints.org} ([35])

On the distribution of linear codes

In this paper, we examine the distribution of binary linear codes in the sense of Manin. For this purpose, we introduce the notions of isolated ratius and complete isolatedness. As a typical example, we calculate the isolated radius of the [7, 4, 3]-Hamming code, and show that it is completely isolated. Using the program in the appendix, we also give a list of isolated radii of some binary linear codes