Determinant code[1] 

Description

Determinant codes give optimal exact repair regenerating codes for any \([n,k,d=k]\) at all the points of the storage bandwidth trade-off curve. The codes are linear, and the exact regenerating property is provided based on fundamental properties of matrix determinants. The field size \(q\) required for this code construction is linear in \(n\).

Decoding

For exact repair, the interior points of the storage-bandwidth trade-off curve can be shown to be the convex hull of \(k\) corner points described by \((\alpha_m,\beta_m)= (\binom{k}{m},\binom{k-1}{m-1})\) for \(m\in\{1,2,\cdots,k\}\).

Parent

References

[1]
M. Elyasi and S. Mohajer, “Determinant Coding: A Novel Framework for Exact-Repair Regenerating Codes”, IEEE Transactions on Information Theory 62, 6683 (2016) DOI
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Zoo Code ID: determinant

Cite as:
“Determinant code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/determinant
BibTeX:
@incollection{eczoo_determinant, title={Determinant code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/determinant} }
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Cite as:

“Determinant code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/determinant

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/matrices/regenerating/determinant.yml.