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.