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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 \(m\in\{1,2,\cdots,k\}\).

Member of code lists

Primary Hierarchy

Classical Domain
Matrix Kingdom
Matrix-based codeECC
Array codeDistributed-storage ECC
Regenerating code (RGC)
Parents
Regenerating code (RGC)
Determinant code

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.), 2026. https://errorcorrectionzoo.org/c/determinant, arXiv:2606.11484
BibTeX:
@incollection{eczoo_determinant,
title={Determinant code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/determinant}
}
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Permanent link:
https://errorcorrectionzoo.org/c/determinant

Cite as:

“Determinant code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/determinant, arXiv:2606.11484

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