Related papers: Multi-point Codes from the GGS Curves
This paper is concerned with the construction of algebraic geometric codes defined from Kummer extensions. It plays a significant role in the study of such codes to describe bases for the Riemann-Roch spaces associated with totally ramified…
We investigate multi-point algebraic geometric codes defined from curves related to the generalized Hermitian curve introduced by Alp Bassa, Peter Beelen, Arnaldo Garcia, and Henning Stichtenoth. Our main result is to find a basis of the…
In this paper, algebraic-geometric (AG) codes associated with the GGS maximal curve are investigated. The Weierstrass semigroup at all $\mathbb F_{q^2}$-rational points of the curve is determined; the Feng-Rao designed minimum distance is…
We determine de Weierstrass semigroup of a pair of certain rational points on the GK-curves. We use this semigroup to obtain two-point AG codes with better parameters than comparable one-point AG codes arising from these curves. These…
In this paper we investigate multi-point Algebraic-Geometric codes associated to the GK maximal curve, starting from a divisor which is invariant under a large automorphism group of the curve. We construct families of codes with large…
For Kummer extensions defined by $y^m = f (x)$, where $f (x)$ is a separable polynomial over the finite field $\mathbb{F}_q$, we compute the number of Weierstrass gaps at two totally ramified places. For many totally ramified places we give…
In this paper we investigate two-point algebraic-geometry codes (AG codes) coming from the Beelen-Montanucci (BM) maximal curve. We study properties of certain two-point Weierstrass semigroups of the curve and use them for determining a…
A method of constructing algebraic-geometric codes with many automorphisms arising from Galois points for algebraic curves is presented.
We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti-Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes…
We present multi-point algebraic geometric codes overstepping the Gilbert-Varshamov bound. The construction is based on the generalized Hermitian curve introduced by A. Bassa, P. Beelen, A. Garcia, and H. Stichtenoth. These codes are…
A classical result states that on a smooth algebraic curve of genus $g$ the number of Weierstrass points, counted with multiplicity, is $g^3-g$. In this paper, we introduce the notion of geometric Weierstrass points of metric graphs and…
A unique decoding algorithm for general AG codes, namely multipoint evaluation codes on algebraic curves, is presented. It is a natural generalization of the previous decoding algorithm which was only for one-point AG codes. As such, it…
We determine the Weierstrass semigroup $H(P_{\infty}, P_{1}, \ldots , P_{m})$ at several points on the $GK$ curve. In addition, we present conditions to find pure gaps on the set of gaps $G(P_{\infty}, P_{1}, \ldots , P_{m})$. Finally, we…
In the realm of algebraic geometric (AG) codes, characterizing dual codes has long been a challenging task. In this paper we introduces a generalized criterion to characterize self-orthogonality of AG codes based on residues, drawing upon…
We compute the Weierstrass semigroup at one totally ramified place for Kummer extensions defined by $y^m=f(x)^{\lambda}$ where $f(x)$ is a separable polynomial over $\mathbb{F}_q$. In addition, we compute the Weierstrass semigroup at two…
In this paper, we examine algebraic geometric (AG) codes associated with curves generated by separated polynomials, and we create AG codes and quantum stabilizer codes from these curves by varying their parameters. Our research involves a…
In this paper, Algebraic-Geometric (AG) codes and quantum codes associated to a family of curves which comprises the famous Suzuki curve are investigated. The Weierstrass semigroup at some rational point is computed. Notably, each curve in…
For a Kummer extension defined by the affine equation $y^{m}=\prod_{i=1}^{r} (x-\a_i)^{\lambda_i}$ over an algebraic extension $K$ of a finite field $\fq$, where $\la_i\in \Z\backslash\{0\}$ for $1\leq i\leq r$, $\gcd(m,q) = 1$, and…
It is always interesting and important to construct non-Reed-Solomon type MDS codes in coding theory and finite geometries. In this paper, we prove that there are non-Reed-Solomon type MDS codes from arbitrary genus algebraic curves. It is…
In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing…