A non-singular plane algebraic curve of degree n(n <=4) is called maximally symmetric if it attains the maximum order of the projective automorphism groups for non-singular plane algebraic curves of degree n. Highly symmetric curves give rise to extremely good error-correcting codes and are ideal for the construction of good universal hash families and authentication. In this work it is proven that the maximally symmetric non-singular plane curves of degree n in P^2 (n not in {4, 6}) are projectively equivalent to the Fermat curve x^n+y^n+z^n.
The Fermat curve x^n + y^n + z^n: the most symmetric non-singular algebraic plane curve
PAMBIANCO, Fernanda
2010
Abstract
A non-singular plane algebraic curve of degree n(n <=4) is called maximally symmetric if it attains the maximum order of the projective automorphism groups for non-singular plane algebraic curves of degree n. Highly symmetric curves give rise to extremely good error-correcting codes and are ideal for the construction of good universal hash families and authentication. In this work it is proven that the maximally symmetric non-singular plane curves of degree n in P^2 (n not in {4, 6}) are projectively equivalent to the Fermat curve x^n+y^n+z^n.File in questo prodotto:
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