Name
Title | ||
|---|---|---|
On the minimum distance and the minimum weight of Goppa codes from a quotient of the Hermitian curve |
Abstract | ||
|---|---|---|
In this paper we study evaluation codes arising from plane quotients of the Hermitian curve, defined by affine equations of the form $y^q+y=x^m$, $q$ being a prime power and $m$ a positive integer which divides $q+1$. The dual minimum distance and minimum weight of such codes are studied from a geometric point of view. In many cases we completely describe the minimum-weight codewords of their dual codes through a geometric characterization of the supports, and provide their number. Finally, we apply our results to describe Goppa codes of classical interest on such curves. |
Year | Venue | Field |
|---|---|---|
2012 | arXiv: Algebraic Geometry | Affine transformation,Integer,Topology,Discrete mathematics,Combinatorics,Of the form,Quotient,Minimum weight,Goppa code,Hermitian matrix,Prime power,Mathematics |
DocType | Volume | Citations |
Journal | abs/1212.0415 | 0 |
PageRank | References | Authors |
0.34 | 5 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Edoardo Ballico | 1 | 16 | 7.15 |
| Alberto Ravagnani | 2 | 32 | 9.46 |