Geodesic
On 3-distance spherical 5-designs
Serdica Mathematical Journal, Tome 46 (2020) no. 2, pp. 165-174.

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Inspired by a recently formulated conjecture by Bannai et al. we investigate spherical codes which admit exactly three differentdistances and are spherical 5-designs. Computing and analyzing distance distributions we provide new proof of the fact (due to Levenshtein) that such codes are maximal and rule out certain cases towards a proof of the conjecture.
Keywords: spherical designs, maximal codes, few distance codes, 05B30, 52C17 
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     title = {On 3-distance spherical 5-designs},
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Boyvalenkov, Peter; Safaei, Navid. On 3-distance spherical 5-designs. Serdica Mathematical Journal, Tome 46 (2020) no. 2, pp. 165-174. http://geodesic.mathdoc.fr/item/SMJ2_2020_46_2_a5/