Construction of linear codes from the unit graph G(ℤn)

Abstract

In this paper, we consider the unit graph [Formula: see text], where [Formula: see text] and [Formula: see text] are distinct primes. For any prime [Formula: see text], we construct [Formula: see text]-ary linear codes from the incidence matrix of the unit graph [Formula: see text] with their parameters. We also prove that the dual of the constructed codes have minimum distance either three or four. Lastly, we stated two conjectures on diameter of unit graph [Formula: see text] and linear codes constructed from the incidence matrix of the unit graph [Formula: see text] for any integer [Formula: see text].