N-ary Codes, Designs, and Enclosings

Two classes of q-ary codes based on group divisible association schemes

By means of Hall's Marriage Theorem, a class of q-ary codes are obtained through block designs based on group divisible association schemes with two associate classes. If these block designs are further semiframes, another class of q-ary codes are also constructed. @ 1999 Elsevier Science B.V. All rights reserved

4-Cycle decompositions of (λ+m)Kv+u \ λKv

In this paper we solve the problem of decomposing (λ+m)K v+u \ λK v for all m > 0 and u > 1. This paper extends the results of "Enclosings of λ-fold 4-cycle systems. "

All q-ary equidistant 3-codes

The elements of {0, 1, . . . , q − 1} are called q-ary codewords of length n over a q-element alphabet. A code is a set of codewords. The Hammingdistance d(c1, c2) of two codewords c1 and c2 is the number of positions where they differ. A code C is called equidistant with distance d if the Hammingdistance of any two codewords is exactly d. Another, shorter name is: q-ary equidistant d-code. The...

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism

Application of fundamental relations on n-ary polygroups

The class of  $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{"o}rnte $n$-arygroups and  a generalization of polygroups. The$beta^*$-relation and the $gamma^*$-relation are the smallestequivalence relations on an $n$-ary polygroup $P$ such that$P/beta^*$ and $P/gamma^*$ are an $n$-ary group and acommutative $n$-ary group, respectively. We use the $beta^*$-...