Generalized EVENODD code

Generalized EVENODD code[1]

Alternative names: Blaum-Bruck-Vardy array code.

Description

Generalized EVENODD code \(\mathcal{EO}_r(m)\) with one horizontal parity column and \(r-1\) independently encoded diagonal-parity columns of different slopes [2].

Protection

For prime \(m\), the \(r=3\) member has minimum column distance four and is therefore an MDS array code; for \(r \geq 4\), the generalized EVENODD family is not MDS in general [2].

Cousin

MDS array code— Generalized EVENODD codes for prime \(m\) and \(r=3\) are MDS array codes [2].

Member of code lists

Classical codes

Primary Hierarchy

Classical Domain

Matrix Kingdom

Matrix-based codeECC

Array codeDistributed-storage ECC

Parents

Array code

Generalized EVENODD code

Children

EVENODD code

Generalized EVENODD codes reduce to EVENODD codes for \(r=2\) [2].

References

[1]: M. Blaum, J. Bruck, and A. Vardy, “MDS array codes with independent parity symbols”, IEEE Transactions on Information Theory 42, 529 (1996) DOI
[2]: M. Blaum, P. G. Farrell, and H. C. A. van Tilborg, “Array codes,” in Handbook of Coding Theory, Vol. II, Part 3, eds. V. S. Pless and W. C. Huffman (Elsevier, 1998), pp. 1855-1909

Page edit log

Victor V. Albert (2024-09-10) — most recent

Cite as:

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

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