In this paper, using some results on the deletion correcting codes, we give an equivalent
form of the Modular Subset-Sum Problem which is of significant importance in computer …

Congruences are ubiquitous in computer science, engineering, mathematics, and related
areas. Develo** techniques for finding (the number of) solutions of congruences is an …

We introduce a general class of codes which includes several well-known classes of
deletion/insertion correcting codes as special cases. For example, the Helberg code, the …

We derive an explicit expression for the weight enumerator of a general class of codes
which includes several classes of deletion correcting codes, such as Helberg, Levenshtein …

We address three questions posed by K. Bibak (2020), and generalize some results of K.
Bibak, DN Lehmer and KG Ramanathan on solutions of linear congruences\(\sum_ {i= 1} …

A comprehensive evaluation system for a camouflage design combining local effect
evaluation and global sampling is developed. Different from previous models, this method …

In this paper, we make a novel connection between information theory and additive
combinatorics; more specifically, between deletion/insertion correcting codes and the …

Abstract Recently, Grynkiewicz et al.(2013), using tools from additive combinatorics and
group theory, proved necessary and sufficient conditions under which the linear congruence …

Let p be a prime and F p be a finite field of p elements. For a 1,..., ak, b∈ F p, let NF p (a 1,...,
an, b) denote the number of the solutions (x 1,..., xn)∈ F pn to the following linear equations …

We call the congruence a 1 x 1+⋯+ akxk≡ b (mod n) an order-restricted linear congruence if
x 1≥⋯≥ x k. What can we say about the number of solutions of these congruences? In this …