28 citations · 70 across the 8 of their papers we have counts for
6 papers · 1 filter
Minimum-weight codewords of the Hermitian codes are supported on complete intersections
Chiara Marcolla, Margherita Roggero
Let be the Hermitian curve defined over a finite field . In this paper we complete the geometrical characterization of the supports of the minimum-w…
Hermitian codes and complete intersections
Chiara Marcolla, Margherita Roggero
In this paper we present a geometrical characterization for the minimum-weight codewords of the Hermitian codes over the fields in the third and fourth phase, na…
Higher Hamming weights for locally recoverable codes on algebraic curves
Edoardo Ballico, Chiara Marcolla
We study the locally recoverable codes on algebraic curves. In the first part of this article, we provide a bound of generalized Hamming weight of these codes. Whereas in the secon…
On the Hermitian curve and its intersections with some conics
Chiara Marcolla, Marco Pellegrini, Massimiliano Sala
We classify completely the intersections of the Hermitian curve with parabolas in the affine plane. To obtain our results we employ well-known algebraic methods for finite fields a…
On the Hermitian curve, its intersections with some conics and their applications to affine-variety codes and Hermitian codes
Chiara Marcolla, Marco Pellegrini, Massimiliano Sala
For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We classify completely the intersections of the Herm…
Improved decoding of affine-variety codes
Chiara Marcolla, Emmanuela Orsini, Massimiliano Sala
General error locator polynomials are polynomials able to decode any correctable syndrome for a given linear code. Such polynomials are known to exist for all cyclic codes and for…