Description
\(q\)-ary linear code with a sparse generator matrix. Alternatively, a member of an infinite family of \([n,k,d]_q\) codes for which the number of nonzero entries in each row and column of the generator matrix are both bounded by a constant as \(n\to\infty\).Cousins
- Dual linear code— The dual of a \(q\)-ary LDPC code has a sparse generator matrix and is called a \(q\)-ary LDGM code.
- \([n,n-1,2]_q\) \(q\)-ary parity-check code— Concatenated \(q\)-ary parity-check codes are LDGM [1].
- \(q\)-ary LDPC code— The dual of a \(q\)-ary LDPC code has a sparse generator matrix and is called a \(q\)-ary LDGM code.
Member of code lists
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References
- [1]
- 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 (2026-06-08) — most recent
- Victor V. Albert (2023-05-04)
Cite as:
“\(q\)-ary LDGM code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/q-ary_ldgm, arXiv:2606.11484