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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