Linear code with complementary dual (LCD)[1] 

Description

A linear code \(C\) admits a complementary dual if \(C\) and its dual code \(C^{\perp}\) do not share any codewords.

Rate

Asymptotically good LCD codes exist [1].

Decoding

The decoding problem reduces to finding the nearest codeword in \(C\) given a word in \(C^{\perp}\) [1].

Parent

Cousin

References

[1]
J. L. Massey, “Linear codes with complementary duals”, Discrete Mathematics 106–107, 337 (1992) DOI
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Zoo Code ID: lcd

Cite as:
“Linear code with complementary dual (LCD)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/lcd
BibTeX:
@incollection{eczoo_lcd, title={Linear code with complementary dual (LCD)}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/lcd} }
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Permanent link:
https://errorcorrectionzoo.org/c/lcd

Cite as:

“Linear code with complementary dual (LCD)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/lcd

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/dual/lcd.yml.