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Optimum distance flag codes from spreads via perfect matchings in graphs

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URI: https://hdl.handle.net/10016/37346
ISSN: 0925-9899
DOI: https://doi.org/10.1007/s10801-021-01086-y
UXXI: AR/0000033012
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Optimum_JAC_2021.pdf (272.88 KB)
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2021-12
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Abstract
In this paper, we study flag codes on the vector space Fnq , being q a prime power and Fq 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 Fnq . 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.
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Network coding, Subspace codes, Spreads, Flag codes, Graphs, Perfect matching
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Alonso-González, C., Navarro-Pérez, M. Á., & Soler-Escrivà, X. (2021). Optimum distance flag codes from spreads via perfect matchings in graphs. Journal of Algebraic Combinatorics, 54(4), 1279-1297.
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