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Flag codes: Distance vectors and cardinality bounds

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URI: https://hdl.handle.net/10016/37288
ISSN: 0024-3795
DOI: https://doi.org/10.1016/j.laa.2022.09.016
UXXI: AR/0000032954
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Flag_Alonso_LAA_2023.pdf (721.99 KB)
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2023-01-01
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Elsevier
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Abstract
Given the finite field with q elements and an integer, a flag is a sequence of nested subspaces of and a flag code is a nonempty set of flags. In this context, the distance between flags is the sum of the corresponding subspace distances. Hence, a given flag distance value might be obtained by many different combinations. To capture such a variability, in the paper at hand, we introduce the notion of distance vector as an algebraic object intrinsically associated to a flag code that encloses much more information than the distance parameter itself. Our study of the flag distance by using this new tool allows us to provide a fine description of the structure of flag codes as well as to derive bounds for their maximum possible size once the minimum distance and dimensions are fixed.
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Network coding, Flag codes, Flag distance, Bounds
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Alonso-González, C., Navarro-Pérez, M. Á., & Soler-Escrivà, X. (2021). Flag codes: Distance vectors and cardinality bounds. Linear Algebra and its Applications, 656, 27-62.
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