Abstract
We present efficient decoding algorithms from square-root errors for two known families of double-circulant codes: A construction based on Sidon sets (Bhargava, Taveres, and Shiva, IEEE IT 74; Calderbank, IEEE IT 83; Guruswami and Li, IEEE IT 2025), and a construction based on cyclic codes (Chen, Peterson, and Weldon, Information and Control 1969). We further observe that the work of Guruswami and Li implicitly gives a transformation from double-circulant codes of certain block lengths to Wozencraft codes which preserves that distance of the codes, and we show that this transformation also preserves efficiency of decoding. By instantiating this transformation with the first family of double-circulant codes based on Sidon sets, we obtain an explicit construction of a Wozencraft code that is efficiently decodable from square-root errors. We also discuss limitations on instantiating this transformation with the second family of double-circulant codes based on cyclic codes.
| Original language | English |
|---|---|
| Pages (from-to) | 4710-4718 |
| Number of pages | 9 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 72 |
| Issue number | 7 |
| DOIs | |
| State | Published - 1 Jul 2026 |
Bibliographical note
Publisher Copyright:© 2026 IEEE.
Keywords
- Error correction codes
- Reed-Muller codes
- binary codes
- decoding
- linear codes
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences
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