\(q\)-ary parity-check code

Description

Also known as a sum-zero code. An \([n,n-1,2]_q\) linear \(q\)-ary code whose codewords consist of the message string appended with a parity-check digit such that the sum over all coordinates of each codeword is zero.

Parents

Cousins

References

[1]
Rudolf Schürer and Wolfgang Ch. Schmid. “Extended Reed–Solomon Code.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. http://mint.sbg.ac.at/desc_CReedSolomon-extended.html
[2]
T. R. Oenning and Jaekyun Moon, “A low-density generator matrix interpretation of parallel concatenated single bit parity codes”, IEEE Transactions on Magnetics 37, 737 (2001). DOI

Zoo code information

Internal code ID: q-ary_parity_check

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Zoo Code ID: q-ary_parity_check

Cite as:
“\(q\)-ary parity-check code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/q-ary_parity_check
BibTeX:
@incollection{eczoo_q-ary_parity_check, title={\(q\)-ary parity-check code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/q-ary_parity_check} }
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Permanent link:
https://errorcorrectionzoo.org/c/q-ary_parity_check

Cite as:

“\(q\)-ary parity-check code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/q-ary_parity_check

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/q-ary_digits/q-ary_parity_check.yml.