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The Exact Second Generalized Covering Radius of Binary Primitive Triple-Error-Correcting BCH Codes

  • Isaac Barouch Essayag
  • Aryeh Lev Zabokritskiy
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Abstract

Let Cm:=BCH(3,m) be the binary primitive triple-error-correcting BCH code of length 2m−1. We determine its second generalized covering radius exactly: R2(Cm)=8 for every m≥5. Equivalently, every two-dimensional syndrome subspace is contained in the binary span of at most eight parity-check columns, and eight columns are necessary in the worst case. This matches the known lower bound.

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Cite

BibTeXRIS
BibTeX
@misc{essayag2026exact,
  title = {{The Exact Second Generalized Covering Radius of Binary Primitive Triple-Error-Correcting BCH Codes}},
  author = {Isaac Barouch Essayag and Aryeh Lev Zabokritskiy},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.07215},
  eprint = {2608.07215},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.07215},
}
RIS
TY  - UNPB
TI  - The Exact Second Generalized Covering Radius of Binary Primitive Triple-Error-Correcting BCH Codes
AU  - Isaac Barouch Essayag
AU  - Aryeh Lev Zabokritskiy
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.07215
UR  - https://arxiv.org/abs/2608.07215
AB  - Let C_m:=BCH(3,m) be the binary primitive triple-error-correcting BCH code of length 2^m−1. We determine its second generalized covering radius exactly: R_2(C_m)=8 for every m≥5. Equivalently, every two-dimensional syndrome subspace is contained in the binary span of at most eight parity-check columns, and eight columns are necessary in the worst case. This matches the known lower bound.
ER  -