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On matroids from self-orthogonal codes and their properties

Weston Loucks and Bahattin Yildiz

Vol. 16 (2023), No. 3, 409–420
Abstract

Matroids and codes are closely related. In the binary case, they are essentially identical. In algebraic coding theory, self-orthogonal codes, and a special type of these called self-dual codes, play an important role because of their connections with t-designs. In this work, we further explore these connections by introducing the notions of cycle-nested and doubly even matroids. In the binary case, we characterize the cocycle-nested matroids and describe some properties of doubly even matroids by relating them to doubly even codes. We also relate the concept of self-orthogonal realizations with Eulerian matroids.

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Keywords
self-orthogonal codes, doubly even codes, self-orthogonal matroids, cocycle, matroids
Mathematical Subject Classification
Primary: 05B35
Secondary: 94B05
Milestones
Received: 9 May 2021
Revised: 24 June 2022
Accepted: 26 June 2022
Published: 10 August 2023

Communicated by Kenneth S. Berenhaut
Authors
Weston Loucks
Northland Preparatory Academy
Flagstaff, AZ
United States
Bahattin Yildiz
Intel Labs
Santa Clara, CA
United States