On the geometry of Hermitian one-point codes
Edoardo Ballico, Alberto Ravagnani
TL;DR
This paper explores the algebraic geometry of Hermitian one-point codes, characterizing minimum-weight codewords and describing small-weight codewords to deepen understanding of their structure.
Contribution
It provides a detailed geometric analysis of Hermitian one-point codes and characterizes their minimum-weight and small-weight codewords, offering new insights into their structure.
Findings
Characterization of minimum-weight codewords in dual codes
Description of many small-weight codewords
Enhanced understanding of the algebraic geometry of Hermitian codes
Abstract
In this paper we study the algebraic-geometry of any one-point code on the Hermitian curve. Moreover, we characterize the minimum-weight codewords of some of their dual codes and describe many their small-weight codewords.
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