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Integer-based code

Alternative Names: \(\mathbb{Z}\) code.

Description

Encodes \(K\) states (codewords) into \(n\) integer coordinates, i.e., into a subset of \(\mathbb{Z}^n\).

Protection

A common distance between integer vectors is the \(\ell_1\) distance [1,2].

Cousin

  • Rotor code— Rotor codes are quantum counterparts of integer codes.

Member of code lists

Primary Hierarchy

Classical Domain
Analog Kingdom
Analog codeECC
Parents
Analog code
Integer-based code
Children
Simplex integer-based code

References

[1]
R. Varshamov, “A class of codes for asymmetric channels and a problem from the additive theory of numbers”, IEEE Transactions on Information Theory 19, 92 (1973) DOI
[2]
L. G. Tallini and B. Bose, “On L<inf>1</inf>-distance error control codes”, 2011 IEEE International Symposium on Information Theory Proceedings 1061 (2011) DOI
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)

— see instructions

Zoo Code ID: integers_into_integers

Cite as:
“Integer-based code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/integers_into_integers, arXiv:2606.11484
BibTeX:
@incollection{eczoo_integers_into_integers,
title={Integer-based code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/integers_into_integers}
}
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Permanent link:
https://errorcorrectionzoo.org/c/integers_into_integers

Cite as:

“Integer-based code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/integers_into_integers, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/analog/integers/integers_into_integers.yml.