Modular-qudit USt code[1,2]

Description

A modular-qubit code whose codespace consists of a direct sum of a modular-qubit stabilizer codespace and one or more of that stabilizer code's error spaces.

Given a subset \(T\) of coset representatives of \(\mathsf{N}(\mathsf{S})/\mathsf{S}\) of a modular-qudit stabilizer code \(((n,K))\) with codespace \(\mathsf{C}\) and stabilizer group \(\mathsf{S}\), one can construct the modular-qudit USt with codespace \begin{align} \mathsf{C}_{\text{USt}}=\bigoplus_{t\in T}t\mathsf{C}~. \tag*{(1)}\end{align} The parameters of the USt are \(((n,K|T|,d))\), where \(|T|\) is the number of chosen coset representatives. A modular-qudit USt is CSS-like when the underlying stabilizer code is CSS, so the coset representatives from the two classical codes underlying the CSS code.