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valbert4 committed Sep 20, 2024
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Block codes protect from erasures or, more generally, errors acting on a few of the \(n\) subsystems. A block code with \textit{distance} \(d\) detects errors acting on up to \(d-1\) subsystems, and corrects erasure errors on up to \(d-1\) subsystems.
The subsystems that are erased are known to the receiver, and erasures of subsystems at unknown locations are called \textit{deletion errors} \cite{arxiv:2001.08405,arxiv:2004.00814,arxiv:2102.02494,arxiv:2102.03015}.
More general forms of noise are caused by \textit{insertion errors} \cite{arxiv:2001.08405,arxiv:2004.00814,arxiv:2102.02494,arxiv:2102.03015}, where subsystems are inserted into the block, and \texit{synchronization errors} (a.k.a. misalignment) \cite{arxiv:1206.0260}, where the code block is misplaced in a larger block by one or more locations.
More general forms of noise are caused by \textit{insertion errors} \cite{arxiv:2001.08405,arxiv:2004.00814,arxiv:2102.02494,arxiv:2102.03015}, where subsystems are inserted into the block, and \textit{synchronization errors} (a.k.a. misalignment) \cite{arxiv:1206.0260}, where the code block is misplaced in a larger block by one or more locations.
The \textit{weight} of an operator on a tensor-product Hilbert space is the number of subsystems on which the operator acts non-trivially.
For example, an operator acting on two subsystem is called a weight-two operator or a two-body operator.
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