In this paper, using generalized {polya} urn models we find the expected value of the size of a branch in recursive $k$-ary trees. We also find the expectation of the number of nodes of a given outdegree in a branch of such trees.

We use the polynomial method to derive upper and lower bounds on the distance distribution of nonbinary codes in the Hamming space. Applications of the bounds include a better asymptotic upper bound on the weight distribution of Goppa codes from maximal curves, a new upper bound on the size of a q-ary code with a given rth generalized weight, improved estimates of the size of secant spaces of a...

Two strongly seminormal codes over 2s are constructed to prove a conjecture of Ostergard. It is shown that a result of Honkala on ( I C , t)-subnormal codes holds also under weaker assumptions. A lower bound and an upper bound on Kq(n, R), the minimal cardinality of a q-ary code of length n with covering radius R are obtained. These give improvements in seven upper bounds and twelve lower bound...

This paper explores the applications of a recent bound on some Weil-type exponential sums over Galois rings in the construction of codes and sequences. A family of codes over Fp, mostly nonlinear, of length pm+1 and size p2 ·pm(D− D/p ), where 1 ≤ D ≤ pm/2, is obtained. The bound on this type of exponential sums provides a lower bound for the minimum distance of these codes. Several families of...

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.

We develop refinements of the Levenshtein bound in q-ary Hamming spaces by taking into account the discrete nature of the distances versus the continuous behavior of certain parameters used by Levenshtein. The first relevant cases are investigated in detail and new bounds are presented. In particular, we derive generalizations and q-ary analogs of a MacEliece bound. We provide evidence that our...

We consider bounds on the size of families F of subsets of a v-set subject to restrictions modulo a prime p on the cardinalities of the pairwise intersections.We improve the known bound when F is allowed to contain sets of different sizes, but only in a special case. We show that if the bound for uniform families F holds with equality, then F is the set of blocks of what we call a p-ary t-desig...

This paper discusses the complexity of bound consistency on n-ary linear constraint system and investigates the relationship between equivalent binary equation systems from the perspective of bound consistency techniques. We propose an efficient bound consistency enforcing algorithm whose complexity is .In addition, by transforming a binary equation system into solved form, an efficient consist...