In this paper from q-ary perfect codes new completely regular q-ary codes are constructed. In particular, two new ternary completely regular codes are obtained from ternary Golay [11, 6, 5] code. The first [11, 5, 6] code with covering radius ρ = 4 coincides with the dual Golay code and its intersection array is (22, 20, 18, 2, 1; 1, 2, 9, 20, 22) . The second [10, 5, 5] code, with covering rad...

In this paper we extend the defect theorem from words to k-ary labeled trees. Indeed we prove that, if a set of n trees satisses a nontrivial identity, then these trees can be expressed as concatenation of at most n ? 1 trees. Some consequences in the theory of tree codes are derived.

This paper concerns a relationship between soft sets and n-ary polygroups. We consider the notion of an n-ary polygroup as a generalization of a polygroup and apply the notion of soft sets to n-ary polygroups. Some related notions are defined and several basic properties are discussed by using the soft set theory. Furthermore, we propose the homomorphism of n-ary polygroups and investigate the ...

In this paper, we define the strongly compatible relation ε on the (m,n)ary hypermodule M, so that the quotient (M/ε∗, h/ε∗) is an (m,n)-ary module over the fundamental (m,n)-ary ring (R/Γ∗, f/Γ∗, g/Γ∗). Also, we determine a family P (M) of subsets of an (m,n)-ary hypermodule M and we give a sufficient condition such that the geometric space (M,P (M)) is strongly transitive. Mathematics Subject...

The h-extra connectivity is an important parameter to measure the reliability and fault tolerance ability of large interconnection networks. The k-ary ncube is an important interconnection network of parallel computing systems. The 1-restricted connectivity of k-ary n-cubes has been obtained by Chen et al. for k ≥ 4 in [6]. Nevertheless, the h-extra connectivity of 3-ary ncubes has not been obt...

An n-ary operation Q : Σ → Σ is called an n-ary quasigroup of order |Σ| if in the equation x0 = Q(x1, . . . , xn) knowledge of any n elements of x0, . . . , xn uniquely specifies the remaining one. Q is permutably reducible if Q(x1, . . . , xn) = P ( R(xσ(1), . . . , xσ(k)), xσ(k+1), . . . , xσ(n) ) where P and R are (n− k+1)-ary and kary quasigroups, σ is a permutation, and 1 < k < n. Anm-ary ...

A non-decreasing sequence of positive integer weights P ={p1, p2,..., pn} (n = N*(m-1) + 1, N is number of non-leaves of m-ary tree) is called absolutely ordered if the intermediate sequences of weights produced by m-ary Huffman algorithm for initial sequence P on i-th step satisfy the following conditions 2 , , ) ( 1 ) ( − = < + N 0 i p p i m i m . Let T be an m-ary tree of size n and M=M(T) b...

A parity-check matrix for a q -ary repeated-root cyclic code is derived using the Hasse derivative. Then the min imum distance of a q-ary repeated-root cyclic code C is expressecin terms of the min imum distance of a certain simple-root cyclic code C that is determined by C. With the help of this result, several binary repeated-root cyclic codes of lengths up to n = 62 are shown to contain the ...

In this paper we study nearly perfect sequences (NPS) via their connection to direct product difference sets (DPDS). We prove the connection between a p-ary NPS of period n and type γ and a cyclic (n, p, n, n−γ p + γ, 0, n−γ p )-DPDS for an arbitrary integer γ. Next, we present the necessary conditions for the existence of a p-ary NPS of type γ. We apply this result for excluding the existence ...

The family tree of a Galton-Watson branching process may contain N -ary subtrees, i.e. subtrees whose vertices have at least N ≥ 1 children. For family trees without infinite N -ary subtrees, we study how fast N -ary subtrees of height t disappear as t → ∞.