Reynald Lercier

J.-M. Couveignes and R. Lercier. The geometry of some parameterizations and encodings. Advances in Mathematics of Communications, 8(4):437-458, 2014.

We explore parameterizations by radicals of low genera algebraic curves. We prove that for q a prime power that is large enough and prime to 6, a fixed positive proportion of all genus 2 curves over the field with q elements can be parameterized by 3-radicals. This results in the existence of a deterministic encoding into these curves when q is congruent to 2 modulo 3. We extend this construction to parameterizations by l-radicals for small odd integers l, and make it explicit for l=5.

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