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On matroids
from self-orthogonal codes and their properties
Weston Loucks and Bahattin Yildiz |
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Vol. 16 (2023), No. 3, 409–420
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Abstract |
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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 -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
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Mathematical Subject Classification
Primary: 05B35
Secondary: 94B05
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Milestones
Received: 9 May 2021
Revised: 24 June 2022
Accepted: 26 June 2022
Published: 10 August 2023
Communicated by Kenneth S. Berenhaut
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Authors |
| Weston Loucks | |
| Northland Preparatory Academy Flagstaff, AZ United States |
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| Bahattin Yildiz | |
| Intel Labs Santa Clara, CA United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
