Explicit Construction of AG Codes from Generalized Hermitian Curves
Chuangqiang Hu
TL;DR
This paper constructs multi-point algebraic geometric codes from generalized Hermitian curves, surpassing the Gilbert-Varshamov bound, and provides explicit generator matrices and dual code formulas.
Contribution
It introduces a new explicit construction method for AG codes using generalized Hermitian curves, with detailed generator matrices and dual code formulas.
Findings
Codes surpass the Gilbert-Varshamov bound
Dual codes retain similar properties
Explicit formulas for generator matrices and duals
Abstract
We present multi-point algebraic geometric codes overstepping the Gilbert-Varshamov bound. The construction is based on the generalized Hermitian curve introduced by A. Bassa, P. Beelen, A. Garcia, and H. Stichtenoth. These codes are described in detail by constrcting a generator matrix. It turns out that these codes have nice properties similar to those of Hermitian codes. It is shown that the duals are also such codes and an explicit formula is given.
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Taxonomy
TopicsCoding theory and cryptography · Cancer Mechanisms and Therapy