We suggest a general method of the construction of secret-sharing schemes based on orthogonal systems of partial (in particular, everywhere determined) k-ary operations which generalizes some known methods of the construction of such schemes by a nite elds and point the orthogonal systems of k-ary operations respecting to these known schemes. The dierent… (More)
The near-totally conjugate orthogonal quasigroups (near-totCO-quasi-groups), i. e., quasigroups for which there exist five (but there are no six) pairwise orthogonal conjugates, are studied. We consider six types of such quasigroups, connection between them and prove that for any integer n ≥ 7 which is relatively prime to 2, 3 and 5 there exist… (More)
Systems of k-ary operations, k 2, generalizing orthogonal sets are considered. These systems have the following property: every k successive k-ary operations of the system are orthogonal. We call these systems successively orthogonal, establish some properties, give examples and methods of construction of these systems.
In this article we study check character systems that is error detecting codes, which arise by appending a check digit a n to every word a 1 a 2 ...a n−1 : a 1 a 2 ...a n−1 → a 1 a 2 ...a n−1 a n with the check formula (...((a 1 · δa 2) · δ 2 a 3)...) · δ n−2 a n−1) · δ n−1 a n = c, where Q(·) is a quasigroup or a loop, δ is a permutation of Q, c ∈ Q. We… (More)