The prefixed Varshamov-Tenengolts (VT) codes, which are subsets of VT codes with
predetermined prefixes, can be used for error correction over segmented edit channels. In …

In this paper, we propose a newly constructed binary code to correct one deletion and one
insertion error that simultaneously occur at any position in a codeword. We first investigated …

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 …

Motivated by the sequence reconstruction problem initiated by Levenshtein, reconstruction
codes were introduced by Cai et al. to combat errors when a fixed number of noisy channels …

This paper proposes a novel binary code to correct one insertion and at most two
consecutive deletion errors simultaneously occurring in a codeword. Our proposed code is …

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} …

Ramanujan sums have attracted significant attention in both mathematical and engineering
disciplines due to their diverse applications. In this paper, we introduce an algebraic …

In this work, we present a novel binary code design to address a single indel error or the
occurrence of simultaneous deletion and insertion errors within a codeword. Our study …

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 …