On the geometry of small weight codewords of dual algebraic geometric codes
Claudio Fontanari, Chiara Marcolla
TL;DR
This paper explores the geometric structure of small weight codewords in dual algebraic geometric codes, especially Hermitian codes, using advanced tools to extend previous findings.
Contribution
It applies Couvreur's methods to analyze the geometry of small weight codewords, extending prior results for Hermitian codes.
Findings
Characterization of small weight codewords' support geometry
Extension of previous results on Hermitian codes
Application of Couvreur's tools to algebraic geometric codes
Abstract
We investigate the geometry of the support of small weight codewords of dual algebraic geometric codes on smooth complete intersections by applying the powerful tools recently developed by Alain Couvreur. In particular, by restricting ourselves to the case of Hermitian codes, we recover and extend previous results obtained by the second named author joint with Marco Pellegrini and Massimiliano Sala.
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