510 research outputs found
Weights in Codes and Genus 2 Curves
We discuss a class of binary cyclic codes and their dual codes. The minimum
distance is determined using algebraic geometry, and an application of Weil's
theorem. We relate the weights appearing in the dual codes to the number of
rational points on a family of genus 2 curves over a finite field
Profinite completions of Burnside-type quotients of surface groups
Using quantum representations of mapping class groups we prove that profinite
completions of Burnside-type surface group quotients are not virtually
prosolvable, in general. Further, we construct infinitely many finite simple
characteristic quotients of surface groups.Comment: revised version, 17
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