International Association for Cryptologic Research

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Proximity Gaps in Interleaved Codes

Authors:
Benjamin E. Diamond , Irreducible
Angus Gruen , Polygon
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DOI: 10.62056/a0ljbkrz
URL: https://cic.iacr.org/p/1/4/8
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Abstract:

A linear error-correcting code exhibits proximity gaps if each affine line of words either consists entirely of words which are close to the code or else contains almost no such words. In this short note, we prove that for each linear code which exhibits proximity gaps within the unique decoding radius, that code's interleaved code also does. Combining our result with a recent argument of Angeris, Evans and Roh ('24), we extend those authors' sharpening of the tensor-based proximity gap of Diamond and Posen (Commun. Cryptol. '24) up to the unique decoding radius, at least in the Reed–Solomon setting.

BibTeX
@article{cic-2025-34901,
  title={Proximity Gaps in Interleaved Codes},
  journal={cic},
  publisher={International Association for Cryptologic Research},
  volume={1, Issue 4},
  url={https://cic.iacr.org/p/1/4/8},
  doi={10.62056/a0ljbkrz},
  author={Benjamin E. Diamond and Angus Gruen},
  year=2025
}