Parameterized codes over graphs
Jorge Neves, Maria Vaz Pinto
TL;DR
This paper reviews known results on parameterized linear codes over graphs, focusing on their parameters like dimension, regularity, and minimum distance, and explores new combinatorial formulas related to their dimension.
Contribution
It provides a detailed review of existing results and introduces new combinatorial formulas for the parameter dimension of these codes.
Findings
Connection between parameter dimension and Eulerian ideals in the ternary case
New combinatorial formulas for the parameter dimension
Detailed review of parameters like regularity and minimum distance
Abstract
In this article we review known results on parameterized linear codes over graphs, introduced by Renter\'ia, Simis and Villarreal in 2011. Very little is known about their basic parameters and invariants. We review in detail the parameters dimension, regularity and minimum distance. As regards the parameter dimension, we explore the connection to Eulerian ideals in the ternary case and we give new combinatorial formulas.
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