Optimum Distance Flag Codes from Spreads via Perfect Matchings in Graphs
Abstract
In this paper, we study flag codes on the vector space $\mathbb{F}_q^n$, being $q$ a prime power and $\mathbb{F}_q$ the finite field of $q$ elements. More precisely, we focus on flag codes that attain the maximum possible distance (optimum distance flag codes) and can be obtained from a spread of $\mathbb{F}_q^n$. We characterize the set of admissible type vectors for this family of flag codes and also provide a construction of them based on well-known results about perfect matchings in graphs. This construction attains both the maximum distance for its type vector and the largest possible cardinality for that distance.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2020
- DOI:
- 10.48550/arXiv.2005.09370
- arXiv:
- arXiv:2005.09370
- Bibcode:
- 2020arXiv200509370A
- Keywords:
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- Computer Science - Information Theory;
- Mathematics - Combinatorics