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Unary code

Alternative names: Thermometer code.

Description

Trivial code that encodes integers \(0\) through \(n\) into binary strings of length \(n\). The \(i\)th codeword is a string consisting of \(i\) ones followed by \(n-i\) zeroes.

Realizations

Neural networks [1].Birdsong production [2].

Cousin

  • Quantum low-weight check (QLWC) code— A family of approximate non-stabilizer qubit QLWC codes with linear distance and rate has been constructed [3] using unary codes that arise from the Feynman-Kitaev clock construction [4].

References

[1]
S. Kak, “Unary Coding for Neural Network Learning”, (2010) arXiv:1009.4495
[2]
I. R. Fiete and H. S. Seung (2007). “Neural network models of birdsong production, learning, and coding”. New Encyclopedia of Neuroscience. Eds. L. Squire, T. Albright, F. Bloom, F. Gage, and N. Spitzer. Elsevier.
[3]
C. Nirkhe, U. Vazirani, and H. Yuen, “Approximate Low-Weight Check Codes and Circuit Lower Bounds for Noisy Ground States”, LIPIcs, Volume 107, ICALP 2018 107, 91:1 (2018) arXiv:1802.07419 DOI
[4]
A. Kitaev, A. Shen, and M. Vyalyi, Classical and Quantum Computation (American Mathematical Society, 2002) DOI
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Zoo Code ID: unary

Cite as:
“Unary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/unary
BibTeX:
@incollection{eczoo_unary, title={Unary code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/unary} }
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Permanent link:
https://errorcorrectionzoo.org/c/unary

Cite as:

“Unary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/unary

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/easy/unary.yml.