Related Experiment Video
Updated: Jun 25, 2025

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
Published on: March 18, 2019
On the Dimensions of Hermitian Subfield Subcodes from Higher-Degree Places
Sabira El Khalfaoui1, Gábor P Nagy2,3
1Institut de Recherche Mathématique de Rennes-IRMAR-UMR 6625, University Rennes, F-35000 Rennes, France.
Abstract:
The focus of our research is the examination of Hermitian curves over finite fields, specifically concentrating on places of degree three and their role in constructing Hermitian codes. We begin by studying the structure of the Riemann-Roch space associated with these degree-three places, aiming to determine essential characteristics such as the basis. The investigation then turns to Hermitian codes, where we analyze both functional and differential codes of degree-three places, focusing on their parameters and automorphisms. In addition, we explore the study of subfield subcodes and trace codes, determining their structure by giving lower bounds for their dimensions. This presents a complex problem in coding theory. Based on numerical experiments, we formulate a conjecture for the dimension of some subfield subcodes of Hermitian codes. Our comprehensive exploration seeks to deepen the understanding of Hermitian codes and their associated subfield subcodes related to degree-three places, thus contributing to the advancement of algebraic coding theory and code-based cryptography.
Related Concept Videos
Cartesian Vector Notation
Vector Representation of Complex Numbers
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the...
Area Computation by the Alternative Coordinate Method
SFG Algebra
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
Vector Algebra: Method of Components
In many applications, the magnitudes and directions of...
Scalar Notation
Consider a man pulling a rope from a hook in the northeast direction. The...

