Also known as Sum-zero code, Zero-sum code.
Description
An \([n,n-1,2]_q\) linear \(q\)-ary code whose codewords consist of the message string appended with a parity-check or zero-sum check digit such that the sum over all coordinates of each codeword is zero.
Parents
- Reed-Solomon (RS) code — RS codes for \(k=n-1\) are parity-check codes [1].
- Cyclic linear \(q\)-ary code — Since permutations coordinate sums, the cyclic permutation of an SPC codeword is another codeword. The generator polynomial of the code is \(x-1\).
- Maximum distance separable (MDS) code
- Small-distance block code
Child
Cousin
- \(q\)-ary LDGM code — Concatenated \(q\)-ary parity-check codes are LDGM [2].
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
Page edit log
- Victor V. Albert (2022-07-19) — most recent
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