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A Class of Composite Codes with Minimum Distance 8

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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 · 2m, 3 · 2m − 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.

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Authors
  1. I. M. Boyarinov
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  2. I. Martin
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  3. B. Honary
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Boyarinov, I.M., Martin, I. & Honary, B. A Class of Composite Codes with Minimum Distance 8. Problems of Information Transmission 37, 353–364 (2001). https://doi.org/10.1023/A:1013827518409

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