Abstract Given a p-dimensional nonnegative, integral vector α, this paper characterizes the convex hull of the set S of nonnegative, integral vectors x that is lexicographically less than or equal to α. To obtain a finite number of elements in S, the vectors x are restricted to be component-wise upper-bounded by an integral vector u. We show that a linear number of facets is sufficient to descr...

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...

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...

Fractional pebbling is a generalization of black-white pebbling introduced recently. In this reasearch paper we solve an open problem by proving a tight lower bound on the pebble weight required to fractionally pebble a balanced d-ary tree of height h. This bound has close ties with branching programs and the separation of P from NL.

In spread spectrum based watermarking schemes, it is a challenging task to embed multiple bits of information into the host signal. M -ary modulation has been proposed as an effective approach to multibit watermarking. It has been proved that an M -ary modulation based watermarking system outperforms significantly a binary modulation based watermarking system. However, in the existing M -ary mo...

Some n-ary constraints such as the alldiff constraints arise naturally in real fife constraint satisfaction problems (CSP). General purpose filtering algorithms could be applied to such constraints. By taking the semantics of the constraint into account, it is possible to design more efficient filtering algorithms. When the domains of the variables are totally ordered (e.g. all values are integ...

Like classical block codes, a locally repairable code also obeys the Singleton-type bound (we call a locally repairable code optimal if it achieves the Singleton-type bound). In the breakthrough work of [14], several classes of optimal locally repairable codes were constructed via subcodes of Reed-Solomon codes. Thus, the lengths of the codes given in [14] are upper bounded by the code alphabet...

The order bound on generalized Hamming weights is introduced in a general setting of codes on varieties which comprises both the one point geometric Goppa codes as the q-ary Reed-Muller codes. For the latter codes it is shown that this bound is sharp and that they satisfy the double chain condition.

The paper gives an upper bound on the size of a q-ary code of length n that has the k-identifiable parent property. One consequence of this bound is that the optimal rate of such a code is determined in many cases when q →∞ with k and n fixed.