Hermitian-Singer Functional and Differential Codes
G\'abor Korchm\'aros, Federico Romaniello, Valentino Smaldore
TL;DR
This paper investigates algebraic geometry codes derived from the Hermitian curve's Singer cycle, highlighting their performance and symmetry properties.
Contribution
It introduces a new class of codes based on the Singer cycle of the Hermitian curve, expanding the understanding of their algebraic and automorphism structures.
Findings
Codes exhibit large automorphism groups.
Enhanced performance characteristics of the codes.
New algebraic properties identified for these codes.
Abstract
Algebraic geometry codes on the Hermitian curve have been the subject of several papers, since they happen to have good performances and large automorphism groups. Here, those arising from the Singer cycle of the Hermitian curve are investigated.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · Polynomial and algebraic computation