A q-ary maximum distance separable (MDS) code C with length n, dimension k over an alphabet A of size q is a set of qk codewords that are elements of An, such that the Hamming distance between two distinct codewords in C is at least n− k+1. Sets of mutually orthogonal Latin squares of orders q ≤ 9, corresponding to two-dimensional q-ary MDS codes, and q-ary one-error-correcting MDS codes for q ...

In general, an n-ary predicate (relation) describes the relationship among its arguments, and such that no argument has to be of a special mode. The uniication and the resolution (SLDNF-resolution) do capture this state of aaair. Hence, the aim of logic programming is in some point approximatively achieved if the system is able to automatically determine the descriptive mode of an n-ary predica...

In this paper, we investigate the fault-tolerant capabilities of the k-ary n-cubes for even integer k with respect to the hamiltonian and hamiltonian-connected properties. The k-ary n-cube is a bipartite graph if and only if k is an even integer. Let F be a faulty set with nodes and/or links, and let k 3 be an odd integer. When |F | 2n−2, we show that there exists a hamiltonian cycle in a wound...

The notion of absorption was developed a few years ago by Barto and Kozik and immediately found many applications, particularly in topics related to the constraint satisfaction problem. We investigate the behavior of absorption in semigroups and n-ary semigroups (that is, algebras with one n-ary associative operation). In the case of semigroups, we give a simple necessary and sufficient conditi...

We define an interconnection network AQn,k which we call the augmented kary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube AQn,k has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n...

N -ary queries in trees select sets of n-tuples of nodes. We propose and investigate representation formalisms for n-ary queries by tree automata, both for ranked and unranked trees. We show that existential run-based queries capture MSO in the n-ary case, as well as universal run-based queries. We then characterize queries by runs of unambiguous tree automata, and show how to decide whether an...

Through the incorporation of derived classes and associations in class diagrams, this paper proposes a method to improve the specification power of multiplicity for n-ary associations in Unified Modeling Language (UML). The enhanced method can specify more business rules explicitly and concisely in class diagrams through the use of multiplicities instead of using constraints defined informally ...

One of key issues for α-n(t) ary resolution automated reasoning based on lattice-valued logic with truthvalue in a lattice implication algebra is to investigate the α-n(t) ary resolution of some generalized literals. In this article, the determination of α-resolution of any 3-ary generalized literals which include the implication operators not more than 2 in LP(X). It not only lay the foundatio...

In the paper, new and easy-to-compute closedform expressions for average symbol error probability of digital M -ary chirp communication system impaired by additive white Gaussian noise and fading are derived. Three fading environments, Rayleigh, Nakagami-m, and generalized-K, that represent most practical wireless channels are considered. The closed-form expressions derived are then used to ill...

In this paper, given a q-ary LCZ sequence set with parameters (N,M,L, ǫ) and even q, we construct another q-ary LCZ sequence set with parameters (2N, 2M,L, 2ǫ) when q is even. Especially for odd L such that L|N , if a q-ary optimal LCZ sequence set with parameters (N,M,L, 1) is used, the new set with parameters (2N, 2M,L, 2) can be optimal in terms of the set size.