Corpus ID: 235446534

On cyclic algebraic-geometry codes

@article{Cabana2021OnCA,
  title={On cyclic algebraic-geometry codes},
  author={Gustavo Cabana and M. Chara and Ricardo A. Podest'a and R. Toledano},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.08884}
}
In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms. We prove that cyclic algebraic geometry codes constructed in this way are closely related to cyclic extensions. We also give a detailed study of the monomial equivalence of cyclic algebraic geometry codes constructed with our method in the case of a rational… Expand

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References

SHOWING 1-10 OF 19 REFERENCES
Which linear codes are algebraic-geometric?
TLDR
An infinite series of curves is constructed in order to show that all linear codes can be obtained from curves using Goppa's construction, and it is proven that this triple is in a certain sense unique in the case of the (7,4,3) code. Expand
Algebraic function fields and codes
TLDR
This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded and contains numerous exercises that help the reader to understand the basic material. Expand
On automorphisms of geometric Goppa codes
The algebraic geometric codes which were introduced by V. D. Goppa in 1977 [7,8]-we call them geometric Goppa codes--can be used to prove the existence of long linear codes which are better than theExpand
Block transitive codes attaining the Tsfasman–Vladut–Zink bound
TLDR
It is proved by using towers of algebraic function fields with either wild or tame ramification, that there are sequences of codes in this family attaining the Tsfasman–Vladut–Zink bound over finite fields of square cardinality. Expand
Orbits of Galois Invariant n-Sets of P1 under the Action of PGL2
For any finite field k we count the number of orbits of galois invariant n-sets of P1(k?) under the action of PGL2(k). For k of odd characteristic, this counts the number of k-points of the moduliExpand
Algebraic Curves Over Finite Fields
Let L(t) = 1+a1t+ · · ·+a2gt be the numerator of the zeta function of an algebraic curve C defined over the finite field Fq of genus g. We show that the coefficients ar of L(t) satisfy certainExpand
Codes on Algebraic Curves
TLDR
Reading this book as soon as possible will lead you to always think more and more, and this book will be always right for you. Expand
Algebra
THIS is a text–book intended primarily for undergraduates. It is designed to give a broad basis of knowledge comprising such theories and theorems in those parts of algebra which are mentioned in theExpand
Transitive and Self-dual Codes Attaining the Tsfasman-Vladut-Zink Bound
We introduce - as a generalization of cyclic codes - the notion of transitive codes, and we show that the class of transitive codes is asymptotically good. Even more, transitive codes attain theExpand
Algebraic Geometry Codes
• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official publishedExpand
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