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Linear Complementary dual codes and Linear Complementary pairs of AG codes in function fields
Alonso S. Castellanos, Adler V. Marques, Luciane Quoos
In recent years, linear complementary pairs (LCP) of codes and linear complementary dual (LCD) codes have gained significant attention due to their applications in coding theory an…
Weierstrass Semigroup, Pure Gaps and Codes on Function Fields
Alonso S. Castellanos, Erik A. R. Mendoza, Luciane Quoos
We determine the Weierstrass semigroup at one and two totally ramified places in a Kummer extension defined by the affine equation over , t…
Locally recoverable codes from automorphism groups of function fields of genus
Daniele Bartoli, Maria Montanucci, Luciane Quoos
A Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we hav…
Explicit Maximal and Minimal Curves of Artin-Schreier Type from Quadratic Forms
Daniele Bartoli, Luciane Quoos, Zülfükar Saygı +1
In this work we present explicit examples of maximal and minimal curves over finite fields in odd characteristic. The curves are of Artin-Schreier type and the construction is clos…
On the difference between permutation polynomials over finite fields
Nurdagül Anbar, Almasa Oduzak, Vandita Patel +3
The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that if , then there is no complete mapping polynomial in $\Fp[x]$ of degree $d…
Maximal curves from subcovers of the GK-curve
Massimo Giulietti, Luciane Quoos, Giovanni Zini
For every with a prime power greater than , the GK-curve is an -maximal curve that is not -covered by the Hermitian curve. In this…