Construction of Linear Codes from the Unit Graph $G(Zₙ⊕ Zₘ)$

In this paper, we develop the python code for generating unit graph G(Zₙₘ), for any integers $m\ & \ n$. For any prime r, we construct r-ary linear codes from the incidence matrix of the unit graph G(Zₙₘ), where $n \ & \ m$ are either power of prime or product of power of primes. We also prove the minimum distance of dual of the constructed codes as either 3 or 4. Finally, we state conjectures two on linear codes constructed from the unit graph G(Zₙ⊕ Zₘ), for any integer $m\ & \ n$.