Author

K. Hansda

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Preprint Oct 2026

Graph-Based Linear Codes Associated with the Finite Ring $\mathbb{F}_p[x]/\langle x^4 \rangle$

We investigate the linear codes derived from the zero-divisor graph $\Gamma(R)$ of the finite local ring $R = \mathbb{F}_p[x]/\langle x^4 \rangle$ for an odd prime $p$. Using an equitable partition of $Z^*(R)$, we determine the parameters of the binary incidence code of $\Gamma(R)$ and construct induced bipartite subgr...

A. Sarkar, K. Hansda, Makhan Maji · 0 citations

Preprint Sep 2026

Cyclic Codes of Length 7_p^s over F_p^m + uF_p^m : Characterization, Duals, and Applications to Quantum and LCD Codes

Let $R_2 = \mathbb{F}_{p^m} + u\mathbb{F}_{p^m}$ ($u^2 = 0$), where $p$ is an odd prime and $m, s \in \mathbb{N}$. For $p \equiv 3, 5 \pmod 7$ with $\gcd(m, 6) = 1$, the cyclotomic polynomial $\Phi_7(x)$ is irreducible over $\mathbb{F}_{p^m}$. This yields a direct sum decomposition $C = C_1 \oplus C_2$ for any cyclic c...

Payel Chandra, K. Hansda · 0 citations