This paper gives two necessary and sufficient conditions of invariants of an m-ary form and one necessary and sufficient condition of covariants of an m-ary form. By these criterions we compute some invariants and covariants of anm-ary form. At last, two examples of computing the syzygies of invairants by the characteristic set method are given.

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 → ∞.

This paper deals with hypergroupoids obtained from n-ary relations. We give conditions for an n-ary relation such that the hypergroupoid associated with it is a hypergroup. First we analyze this construction using a ternary relation and then we generalize it for an n-ary relation.

Performance analysis schemes for wide-band -ary frequency-shift keying systems with a limiter-discriminator-integrator receiver are presented along with analysis and simulation results for 4-ary and 8-ary systems. The probability distribution of clicks is required for performance analysis and is determined in this letter for Rayleigh fading channels.

This is a survey of the results obtained by K. G lazek and his co-workers. We restrict our attention to the problems of axiomatizations of n-ary groups, classes of n-ary groups, properties of skew elements and homomorphisms induced by skew elements, constructions of covering groups, classifications and representations of n-ary groups. Some new results are added too.

For $$m\ge 4$$ even, the duals of p-ary codes, for any prime p, from adjacency matrices m-ary 2-cube $$Q^m_2$$ are shown to have subcodes with parameters $$[m^2,2m-2,m]$$ which minimal PD-sets size $$\frac{m}{2}$$ constructed, hence attaining full error-correction capabilities code, and, as such, most efficient sets permutation decoding.

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 di erent transformations of orthogonal systems o...

We design 4-ary codebooks using Reed Muller codes for multiple-input multiple-output (MIMO) beamforming systems. An upperbound on the maximum correlation magnitude metric of a 4-ary codebook is derived from the minimum Hamming distance of the corresponding binary linear block code. The 4-ary MIMO beamforming codebooks for the number of transmit antennas equal to 4, 8, 16, and 32 are tabulated. ...

We present an algorithm for finding a system of recurrence relations for the number of k-ary words of length n that satisfy a certain set of conditions. A rewriting of these relations automatically gives a system of functional equations satisfied by the multivariate generating function that counts k-ary words by their length and the indices of the corresponding recurrence relations. We propose ...