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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 \(T_1=(-1/3,-1/6) \cup (1/6,1/3)\) . We also prove the universal optimality of these configurations among all codes whose distance-avoiding set is \(T_2=(-1/2,-1/3) \cup (1/3,1/2)\) .

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Energy of Codes with Forbidden Distances in 48 Dimensions

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  • 发表日期：

    2026年

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  • Peter G. Boyvalenkov,
  • Peter D. Dragnev

摘要

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 \(T_1=(-1/3,-1/6) \cup (1/6,1/3)\) . We also prove the universal optimality of these configurations among all codes whose distance-avoiding set is \(T_2=(-1/2,-1/3) \cup (1/3,1/2)\) .