Asymptotics for the number of n-quasigroups of order 4

Abstract

The asymptotic form of the number of n-quasigroups of order 4 is $3^{n+1}{2}^{2^n+1}(1+o(1))$. Keywords: n-quasigroups, MDS codes, decomposability, reducibility.

15 p., 3 fig

Cited by in corpus (14)

• n-Ary quasigroups of order 4
• On the structure of non-full-rank perfect codes
• On decomposability of 4-ary distance 2 MDS codes, double-codes, and n-quasigroups of order 4
• On the number of 1-perfect binary codes: a lower bound
• On reducibility of n-ary quasigroups
• On irreducible n-ary quasigroups with reducible retracts
• A Lower Bound on the Number of Boolean Functions with Median Correlation Immunity
• On connection between reducibility of an n-ary quasigroup and that of its retracts
• On q-ary Bent and Plateaued Functions
• Distance-2 MDS codes and latin colorings in the Doob graphs
• On the number of frequency hypercubes $F^n(4;2,2)$
• On a test on switching separability of graphs modulo $q$
• Characterization of polystochastic matrices of order $4$ with zero permanent
• Asymptotic bounds on the numbers of vertices of polytopes of polystochastic matrices