Smolin-Smith-Wehner (SSW) code[1,2] 


A family of \(((n=4k+2l+3,M_{k,l},2))\) CWS codes, where \(M_{k,l} \approx 2^{n-2}(1-\sqrt{2/(\pi(n-1))})\), whose codewords are superpositions of particular bitstrings and their complements. For \(n \geq 11\), these codes have a logical subspace whose dimension is larger than that of the largest stabilizer code for the same \(n\) and \(d\). A subset of these codes can be augmented to yield codes with one higher logical dimension [3].




J. A. Smolin, G. Smith, and S. Wehner, “Simple Family of Nonadditive Quantum Codes”, Physical Review Letters 99, (2007) arXiv:quant-ph/0701065 DOI
K. Feng and C. Xing, “A new construction of quantum error-correcting codes”, Transactions of the American Mathematical Society 360, 2007 (2007) DOI
S. Yu, Q. Chen, and C. H. Oh, “Graphical Quantum Error-Correcting Codes”, (2007) arXiv:0709.1780
A. Cross et al., “Codeword Stabilized Quantum Codes”, IEEE Transactions on Information Theory 55, 433 (2009) arXiv:0708.1021 DOI
Cross, Andrew William. Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes. Diss. Massachusetts Institute of Technology, 2008.
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Zoo Code ID: ssw

Cite as:
“Smolin-Smith-Wehner (SSW) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.
@incollection{eczoo_ssw, title={Smolin-Smith-Wehner (SSW) code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Smolin-Smith-Wehner (SSW) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.