相关论文: On the automorphism groups of some AG-codes based …
A lot of attention has been paid to the investigation of the algebraic properties of linear codes. In most cases, this investigation involves the determination of required code automorphisms, which are useful for decoders, such as the…
Let $\mathcal{C}$ be a plane curve defined over the algebraic closure $K$ of a prime finite field $\mathbb{F}_p$ by a separated polynomial, that is $\mathcal{C}: A(y)=B(x)$, where $A(y)$ is an additive polynomial of degree $p^n$ and the…
A method of constructing algebraic-geometric codes with many automorphisms arising from Galois points for algebraic curves is presented.
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…
We show that in many cases, the automorphism group of a curve and the permutation automorphism group of a corresponding AG code are the same. This generalizes a result of Wesemeyer beyond the case of planar curves.
For $a,b\geq 3$, we calculate the orders of automorphisms of smooth curves with bidegree $(a,b)$ in the product $\pp$ of the projective line $\mathbb P^1$. We identify smooth curves in $\pp$ which have automorphisms with the largest orders.…
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…
Let $\X$ be an algebraic curve of genus $g \geq 2$ defined over a field $\F_q$ of characteristic $p > 0$. From $\X$, under certain conditions, we can construct an algebraic geometry code $C$. If the code $C$ is self-orthogonal under the…
Expository paper discussing AG or Goppa codes arising from curves, first from an abstract general perspective then turning to concrete examples associated to modular curves. We will try to explain these extremely technical ideas using a…
We investigate the automorphism groups of the algebraic curves \[ \mathcal{C}_d : y^d = \varphi_d(x), \] where $\varphi_d(x)$ denotes the Chebyshev polynomial of degree $d$, defined over a field $k$ with $p:=\operatorname{char}(k) \nmid…
We look at AG codes associated to the projective line, re-examining the problem of determining their automorphism groups (originally investigated by Duer in 1987 using combinatorial techniques) using recent methods from algebraic geometry.…
We present an algorithm to compute the automorphism group of a Mori dream space. As an example calculation, we determine the automorphism groups of singular cubic surfaces with general parameters. The strategy is to study graded…
In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss…
The point of this paper is to use affine automorphisms from algebraic geometry to build cryptographic multivariate mappings. We will construct groups G,H, both isomorphic to the cyclic group with a prime number of elements and multilinear…
In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.
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…
The automorphism groups of various linear codes are extensively studied yielding insights into the respective code structure. This knowledge is used in, e.g., theoretical analysis and in improving decoding performance, motivating the…
In this article we study the automorphism groups of binary cyclic codes. In particular, we provide explicit constructions for codes whose automorphism groups can be described as (a) direct products of two symmetric groups or (b) iterated…
We describe algorithms based on invariant theory to solve problems on the geometry of curves, mainly those of genus 2, 3 and 4. New theoretical results building on the first author's PhD thesis are also included.
Let C be a binary linear code and suppose that its automorphism group contains a non trivial subgroup G. What can we say about C knowing G? In this paper we collect some answers to this question in the cases G=C_p, G=C_2p and G=D_2p (p an…