A proof is presented that shows that the number of directions determined by a function over a finite field GF (q) is either 1, at least (q+3)/2, or between q/s+1 and (q − 1)/(s − 1) for some s where GF (s) is a subfield of GF (q). Moreover the graph of those functions that determine less than half the directions is GF (s)−linear. This completes the unresolved cases s = 2 and s = 3 of the main t...

weight distribution of linear codes over GF (q l) having generator matrices over GF (q)," \New upper bound on the rate of a code via the Delsarte-MacWilliams inequalities," IEEE Trans.

the verb in russian language is a part of speech which involves several grammatical features. regarding methods of expressing the person, we can classify it in two major groups: personal verbs and non-personal verbs. the difference of these two groups is in their expression and inexpression of the person as a grammatical category. the purpose of this research is to consider ways of declaring th...

A partition u of [k] = f1; 2; : : : ; kg is contained in another partition v of [l] if [l] has a k-subset on which v induces u. We are interested in counting partitions v not containing a given partition u or a given set of partitions R. This concept is related to that of forbidden permutations. A strengthening of Stanley{Wilf conjecture is proposed. We prove that the GF counting v is rational ...

A vector space partition of a finite vector space V over the field of q elements is a collection of subspaces whose union is all of V and whose pairwise intersections are trivial. While a number of necessary conditions have been proved for certain types of vector space partitions to exist, the problem of the existence of partitions meeting these conditions is still open. In this note, we consid...

Argumentation can be viewed as a process of generating explanations. We propose a new argumentation semantics, related admissibility, for closely capturing explanations in Abstract Argumentation, and distinguish between compact and verbose explanations. We show that dispute forests, composed of dispute trees, can be used to correctly compute these explanations.