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math.AG2012★ 3 cited
Polar varieties, Bertini's theorems and number of points of singular complete intersections over a finite field
Antonio Cafure, Guillermo Matera, Melina Privitelli
Let P^n denote the n-dimensional projective space defined over the algebraic closure of a finite field F_q, let V contained P^n be a complete intersection defined over F_q of dimen…
math.AG2011★ 11 cited
Singularities of symmetric hypersurfaces and an application to Reed-Solomon codes
Antonio Cafure, Guillermo Matera, Melina Privitelli
We determine conditions on q for the nonexistence of deep holes of the standard Reed-Solomon code of dimension k over F_q generated by polynomials of degree k+d. Our conditions rel…