Tootfinder

Recursive construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic - II
Monika Yadav, Anuradha Sharma
https://arxiv.org/abs/2510.06069

Recursive construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic - II
Let $\mathcal{R}_{e,m}$ be a finite commutative chain ring of even characteristic with maximal ideal $\langle u \rangle$ of nilpotency index $e \geq 2,$ Teichm$\ddot{u}$ller set $\mathcal{T}_{m},$ and residue field $\mathcal{R}_{e,m}/\langle u \rangle$ of order $2^m.$ Suppose that $2 \in \langle u^κ\rangle \setminus \langle u^{κ+1}\rangle$ for some even positive integer $ κ\leq e.$ In this paper, we provide a recursive method to construct a self-orthogonal code $\mathcal{C}_e$ of type $\{λ_…

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Recursive construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic - I
Monika Yadav, Anuradha Sharma
https://arxiv.org/abs/2510.06082

Recursive construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic - I
Let $\mathscr{R}_{e,m}$ denote a finite commutative chain ring of even characteristic with maximal ideal $\langle u \rangle$ of nilpotency index $e \geq 3,$ Teichm$\ddot{u}$ller set $\mathcal{T}_{m},$ and residue field $\mathscr{R}_{e,m}/\langle u \rangle$ of order $2^m.$ Suppose that $2 \in \langle u^κ\rangle \setminus \langle u^{κ+1}\rangle$ for some odd integer $κ$ with $3 \leq κ\leq e.$ In this paper, we first develop a recursive method to construct a self-orthogonal code $\mathscr{D}_e…