Energy of codes with forbidden distances in 48 dimensions
Abstract
We prove the universal optimality of four remarkable spherical 11-designs in 48 dimensions either among all antipodal codes, or all spherical 3-designs, whose inner-products avoid the set T1=(-1/3,-1/6) (1/6,1/3). We also prove the universal optimality of these configurations among all codes whose distance-avoiding set is T2=(-1/2,-1/3) (1/3,1/2).
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