Abstract
An equidistant constant dimension subspace code C is a set of k-dimensional subspaces in a vector space V over the finite field of order q, which pairwise intersect in subspaces of a fixed dimension t. The classical example of an equidistant constant dimension subspace code C is a set of k-spaces, passing through a fixed t-space. This particular example is called a sunflower. The sunflower bound states that if the size of C is larger than \(\left( \frac{q^{k}-q^{t}}{q-1}\right) ^2 + \frac{q^{k}-q^{t}}{q-1} +1\), then C is a sunflower. We improve this sunflower bound for an equidistant constant dimension subspace code C of k-spaces, pairwise intersecting in a 1-space.
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The research of Daniele Bartoli was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA - INdAM). The work of Ago-Erik Riet was partially supported by the COST Action IC1104 Random Network Coding and Designs over GF(q) through a Short Term Scientific Mission, and the Estonian Research Council through the research Grants PSG114, PUT405, PUT620. He would like to thank Ghent University for their hospitality as most of the work was carried out while working in Ghent. The research of P. Vandendriessche is supported by a postdoctoral grant of the FWO-Flanders.
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Bartoli, D., Riet, AE., Storme, L. et al. Improvement to the sunflower bound for a class of equidistant constant dimension subspace codes. J. Geom. 112, 12 (2021). https://doi.org/10.1007/s00022-021-00572-9
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DOI: https://doi.org/10.1007/s00022-021-00572-9