Some Matroids Related to Sum-Rank Metric Codes
Avijit Panja, Rakhi Pratihar, and Tovohery Hajatiana Randrianarisoa
TL;DR
This paper introduces sum-matroids, a new mathematical structure linked to sum-rank metric codes, generalizing matroids and q-matroids, and extends key properties like duality and weights.
Contribution
It defines sum-matroids, establishes their connection to sum-rank metric codes, and generalizes existing results for matroids and q-matroids, including duality theorems.
Findings
Sum-matroids are introduced and linked to sum-rank metric codes.
Generalized weights for sum-matroids are defined.
A Wei-type duality theorem for sum-matroids is proved.
Abstract
We introduce the notion of sum-matroids and show its association with sum-rank metric codes. As a consequence, some results for sum-rank metric codes by Mart\'inez-Pe\~nas are generalized for sum-matroids. The sum-matroids generalize the notions of matroids and -matroids. We define the generalized weights for sum-matroids and prove a Wei-type duality theorem which generalizes the analogous cases for matroids and q-matroids.
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · Graph Labeling and Dimension Problems