Publication: Moderate-density parity-check codes from projective bundles
Moderate-density parity-check codes from projective bundles
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Bariffi, J., Mattheus, S., Neri, A., & Rosenthal, J. (2022). Moderate-density parity-check codes from projective bundles. Designs, Codes and Cryptography, 90(12), 2943–2966. https://doi.org/10.1007/s10623-022-01054-y
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New constructions for moderate-density parity-check (MDPC) codes using finite geometry are proposed. We design a parity-check matrix for the main family of binary codes as the concatenation of two matrices: the incidence matrix between points and lines of the Desarguesian projective plane and the incidence matrix between points and ovals of a projective bundle. A projective bundle is a special collection of ovals which pairwise meet in a unique point. We determine the minimum distance and the dimension of these codes, and we show that
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- Bariffi, Jessica
- Mattheus, Sam
- Neri, Alessandro
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Bariffi, J., Mattheus, S., Neri, A., & Rosenthal, J. (2022). Moderate-density parity-check codes from projective bundles. Designs, Codes and Cryptography, 90(12), 2943–2966. https://doi.org/10.1007/s10623-022-01054-y
