55 citations · 628 across the 77 of their papers we have counts for
5 papers · 1 filter
On the number of 1-perfect binary codes: a lower bound
Denis Krotov, Sergey Avgustinovich
We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is asymptotically tight.
On reconstructing reducible n-ary quasigroups and switching subquasigroups
Denis Krotov, Vladimir Potapov, Polina Sokolova
(1) We prove that, provided n>=4, a permutably reducible n-ary quasigroup is uniquely specified by its values on the n-ples containing zero. (2) We observe that for each n,k>=2 and…
On irreducible n-ary quasigroups with reducible retracts
Denis Krotov
An n-ary operation q:A^n->A is called an n-ary quasigroup of order |A| if in x_0=q(x_1,...,x_n) knowledge of any n elements of x_0,...,x_n uniquely specifies the remaining one. An…
On reducibility of n-ary quasigroups
Denis Krotov
An -ary operation is called an -ary quasigroup of order if in the equation knowledge of any elements of , ..., unique…
Asymptotics for the number of n-quasigroups of order 4
Vladimir Potapov, Denis Krotov
The asymptotic form of the number of n-quasigroups of order 4 is . Keywords: n-quasigroups, MDS codes, decomposability, reducibility.