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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_…

'We blew it up. And we’ll do it again’.
‘I don’t give a shit what you call it.’
These words, of US Secretary of State Marco Rubio and Vice President J.D. Vance, respectively,
refer to the first of five US bombings of boats in international waters near Venezuela in the last month,
which have reportedly killed twenty-seven people overall.
Washington claims the boats were carrying drugs destined for US shores but has offered no proof;
evidence indica…

Gabriel Hetland, Murder in the Caribbean — Sidecar
The campaign against Venezuela.

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…