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Cross-interleaved RS (CIRS) code[1,2]

Description

An IRS code constructed from two shortened RS codes and two forms of interleaving. In a 2D array visualization, one component code runs vertically and the other diagonally [3].

Protection

Can correct burst errors by first decoding one RS component and then treating residual failures as erasures for the other component [3].

Realizations

Compact discs (CDs); see [3][4; Sec. 5.6][5; Ch. 4].

Cousin

  • Array code— The CIRS code can also be visualized as a 2D array code [3].

Member of code lists

Primary Hierarchy

Classical Domain
Galois-field Kingdom
\(q\)-ary codeECC
Additive \(q\)-ary codeECC
Linear \(q\)-ary codeECC
Interleaved RS (IRS) code
Parents
Interleaved RS (IRS) code
Cross-interleaved RS (CIRS) code

References

[1]
L. B. Vries and K. Odaka, 1982, June, “CIRC-the error-correcting code for the compact disc digital audio system”. In Audio Engineering Society Conference: 1st International Conference: Digital Audio. Audio Engineering Society
[2]
K. Odaka, Y. Sako, I. Iwamoto, T. Doi, and L. B. Vries, “Error Correctable Data Transmission Method”, U.S. Patent US4413340A (1983)
[3]
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
[4]
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes (Cambridge University Press, 2003) DOI
[5]
S. B. Wicker and V. K. Bhargava, “Reed-Solomon Codes and Their Applications”, (1999) DOI
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)

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Zoo Code ID: cross_interleaved_reed_solomon

Cite as:
“Cross-interleaved RS (CIRS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/cross_interleaved_reed_solomon, arXiv:2606.11484
BibTeX:
@incollection{eczoo_cross_interleaved_reed_solomon,
title={Cross-interleaved RS (CIRS) 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/cross_interleaved_reed_solomon}
}
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Permanent link:
https://errorcorrectionzoo.org/c/cross_interleaved_reed_solomon

Cite as:

“Cross-interleaved RS (CIRS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/cross_interleaved_reed_solomon, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/ag/reed_solomon/irs/cross_interleaved_reed_solomon.yml.