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PreprintCC BY-NC-ND 4.0arXiv

A new upper bound for Sidon sets in 𝔽24k+3

  • Darrion Thornburgh
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Abstract

A subset S ⊆ 𝔽2n is called a Sidon set if no four distinct points of S have zero sum. It is shown that if n ≥ 7 and n ≡ 3 mod 4, then |S|≤ 2(n+1)/2−3. As a consequence, for any even t ≥ 4, there does not exist a binary linear [2t−3,2t−2t−2,5]-code, strengthening a nonexistence result of Brouwer and Tolhuizen from 1993. As a second consequence, we also show that for an even integer n ≥ 4, every almost perfect nonlinear (APN) function F : 𝔽2n → 𝔽2n has nonlinearity at least $3$.

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Cite

BibTeXRIS
BibTeX
@misc{thornburgh2026upper,
  title = {{A new upper bound for Sidon sets in $\mathbbF_2^4k+3$}},
  author = {Darrion Thornburgh},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27731},
  eprint = {2609.27731},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27731},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A new upper bound for Sidon sets in 𝔽_2^4k+3
AU  - Darrion Thornburgh
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27731
UR  - https://arxiv.org/abs/2609.27731
AB  - A subset S ⊆ 𝔽_2^n is called a Sidon set if no four distinct points of S have zero sum. It is shown that if n ≥ 7 and n ≡ 3 mod 4, then |S|≤ 2^(n+1)/2−3. As a consequence, for any even t ≥ 4, there does not exist a binary linear [2^t−3,2^t−2t−2,5]-code, strengthening a nonexistence result of Brouwer and Tolhuizen from 1993. As a second consequence, we also show that for an even integer n ≥ 4, every almost perfect nonlinear (APN) function F : 𝔽_2^n → 𝔽_2^n has nonlinearity at least $3$.
ER  -