A Class of Composite Codes with Minimum Distance 8

A Class of Composite Codes with Minimum Distance 8 We consider linear composite codes based on the |a+x|b+x|a+b+x| construction. For m ≥ 3 and r ≤ 4m + 3, we propose a class of linear composite [3 · 2 m , 3 · 2 m − r, 8] codes, which includes the [24,12,8] extended Golay code. We describe an algebraic decoding algorithm, which is valid for any odd m, and a simplified version of this algorithm, which can be applied for decoding the Golay code. We give an estimate for the combinational-circuit decoding complexity of the Golay code. We show that, along with correction of triple independent errors, composite codes with minimum distance 8 can also correct single cyclic error bursts and two-dimensional error bytes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

A Class of Composite Codes with Minimum Distance 8

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/A:1013827518409
Publisher site
See Article on Publisher Site

Abstract

We consider linear composite codes based on the |a+x|b+x|a+b+x| construction. For m ≥ 3 and r ≤ 4m + 3, we propose a class of linear composite [3 · 2 m , 3 · 2 m − r, 8] codes, which includes the [24,12,8] extended Golay code. We describe an algebraic decoding algorithm, which is valid for any odd m, and a simplified version of this algorithm, which can be applied for decoding the Golay code. We give an estimate for the combinational-circuit decoding complexity of the Golay code. We show that, along with correction of triple independent errors, composite codes with minimum distance 8 can also correct single cyclic error bursts and two-dimensional error bytes.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 9, 2004

References

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