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

In this paper, we develop the python code for generating unit graph [Formula: see text], for any positive integers [Formula: see text] and [Formula: see text]. For any prime number [Formula: see text], we construct [Formula: see text]-ary linear codes from the incidence matrix of the unit graph [Formula: see text], where [Formula: see text] and [Formula: see text] are either powers of prime or product of power of primes. We also prove the minimum distance of dual of the constructed codes is either 3 or 4. Finally, we state two conjectures on linear codes constructed from the unit graph [Formula: see text], for any integer [Formula: see text] and [Formula: see text].