We determine the dimension of certain q-ary algebraic-geometric trace codes, extending previous results of Van Der Vlugt for p-ary algebraicgeometric trace codes.

The characterization and construction of bent functions are challenging problems. The paper generalizes the constructions of Boolean bent functions by Mesnager [33], Xu et al. [40] and p-ary bent functions by Xu et al. [41] to the construction of p-ary weakly regular bent functions and presents new infinite families of p-ary weakly regular bent functions from some known weakly regular bent func...

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...

For any given k, the sequence of k-ary Catalan numbers, Ct,k = 1 kt+1 ( kt t ) , enumerates a number of combinatorial objects, including k-ary Dyck words of length n = kt and k-ary trees with t internal nodes. We show that these objects can be efficiently ordered using the same variation of lexicographic order known as cool-lex order. In particular, we provide loopless algorithms that generate ...

When n is odd, a cohomology of type Hochschild for n-ary partially associative algebras has been defined in Gnedbaye’s thesis. Unfortunately, the cohomology definition is not valid when n is even. This fact is found again in the computations of the n-ary partially associative free algebra. In this work, we define in a first time two approachs of an Hochschild cohomology for n-ary partially asso...