Unary code 

Also known as Thermometer code.

Description

Trivial code that encodes integers \(1\) 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].

Parent

Cousin

  • Quantum low-weight check (QLWC) code — A family of approximate non-stabilizer 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]
Fiete, I. R., & Seung, H. S. (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”, (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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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.