The Gilbert-Varshamov (GV) lower bound on the maximum cardinality of a q-ary code of length n with minimum Hamming distance at least d can be obtained by application of Turán’s theorem to the graph with vertex set {0, 1, . . . , q − 1}n in which two vertices are joined if and only if their Hamming distance is at least d. We generalize the GV bound by applying Turán’s theorem to the graph with v...

We obtain an upper bound on the number of extended irreducible q-ary Goppa codes of degree r and length q + 1, where q = p and n and r > 2 are prime numbers.

We propose new intersection problems in the q-ary n-dimensional hypercube. The answers to the problems include the Katona’s t-intersection theorem and the Erdős–Ko–Rado theorem as special cases. We solve some of the basic cases of our problems, and for example we get an Erdős–Ko–Rado type result for t-intersecting k-uniform families of multisets with bounded repetitions. Another example is obta...

this paper deals with a multi-period fixed charge production-distribution problem associated with backorder and inventories. the objective is to determine the size of the shipments from each supplier and backorder and inventories at each period, so that the total cost incurred during the entire period towards production, transportation, backorder and inventories is minimised. a 0-1 mixed intege...

Until now single values of IRR are traditionally used to estimate the time value of cash flows. Since uncertainty exists in estimating cost data, the resulting decision may not be reliable. The most commonly cited drawbacks to using the internal rate of return in evaluatton of deterministic cash flow streams is the possibility of multiple conflicting internal rates of return. In this paper we p...

A Sharp lower bound is derived for the cyclic list distance between two codewords, having Hamming distance , in the standard -ary Gray code of length , for 1 and for even values of . The bound generalizes a similar result in the binary case.

In this paper, we first introduce the concepts of G-systems, quotient G-systems and isomorphism theorems on G-systems of n-ary semihypergroups . Also we consider the Green's equivalences on G-systems and further in-vestigate some of their properties. A number of n-ary semihypergroups are constructed and presented as examples in this paper.

Let b ≥ 2 be an integer and ξ be an irrational real number. Among other results, we establish an explicit lower bound for the number of distinct blocks of n digits occurring in the b-ary expansion of ξ.