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arXiv · 2402.11257

Construction of Linear Codes from the Unit Graph $G(\mathbb{Z}_{n}\oplus \mathbb{Z}_{m})$

Wajid M. Shaikh·Rupali S. Jain·B. Surendranath Reddy
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Abstract

In this paper, we develop the python code for generating unit graph $G(\mathbb{Z}_{n}\oplus\mathbb{Z}_{m})$, for any integers $m\ \& \ n$. For any prime $r$, we construct $r$-ary linear codes from the incidence matrix of the unit graph $G(\mathbb{Z}_{n}\oplus\mathbb{Z}_{m})$, 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 $G(\mathbb{Z}_{n}\oplus \mathbb{Z}_{m})$, for any integer $m\ \& \ n$.

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Wajid M. Shaikh, Rupali S. Jain, B. Surendranath Reddy. 2024-02-17. Construction of Linear Codes from the Unit Graph $G(\mathbb{Z}_{n}\oplus \mathbb{Z}_{m})$. https://arxiv.org/abs/2402.11257

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