A. Garcia and R. Lax, Goppa codes and Weierstrass gaps, Coding theory and algebraic geometry, Lectures Notes in Mathematics, Vol. 1518 Springer-Verlag, Berlin– ...

Pure gaps are very useful in the construction of algebraic-geometry codes and are related to improvements on the Goppa bound of the minimum distance of these ...

We generalize results of Homma and Kim [J. Pure Appl. Algebra Vol. 162, (2001), pp. 273--290] concerning an improvement on the Goppa bound on the minimum ...

where (F −D) is the F-space of differentials η on X such that η=0 or div(η). F − D. The dimension of C can be estimated using the Riemann-Roch theorem.

ABSTRACT Goppa codes are linear codes arising from algebraic curves over finite fields. Sufficient conditions are given ensuring that all automorphisms of a ...

Abstract: We prove that if there are consecutive gaps at a rational point on a smooth curve defined over a finite field, then one can improve the usual lower ...

Jun 10, 2024 · One-point geometric Goppa codes are defined as the algebraic geometric codes \(C(D,G)\) where \(G=\mu Q\) is a multiple of a single point.

Sufficient conditions are given ensuring that all automorphisms of a Goppa code are inherited from the automorphism group of the curve. In some cases, these ...

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Abstract. We prove that elements of the Weierstrass gap set of a pair of points may be used to define a geometric Goppa code which has minimum.