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Abstract Two d -dimensional simplices in Rᵈ R d are neighborly if its intersection is a (d-1) (d - 1) -dimensional set. A family of d -dimensional simplices in Rᵈ R d is called neighborly if every two simplices of the family are neighborly. Let Sd S d be the maximal cardinality of a neighborly family of d -dimensional simplices in Rᵈ R d. Based on the structure of some codes V \0, 1, *\ⁿ V ⊂ 0, 1, ∗ n it is shown that ₃ (2^d+1-Sd) = lim d → ∞ (2 d + 1 - S d) = ∞. Moreover, a result on the structure of codes V \0, 1, *\ⁿ V ⊂ 0, 1, ∗ n is given.
Andrzej P. Kisielewicz (Mon,) studied this question.