Intersection of Hamming codes avoiding Hamming subcodes

J. Rifà, F. I. Solov'Eva, M. Villanueva

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

We prove that given a binary Hamming code Hn of length n = 2 m - 1, m ≥ 3, or equivalently a projective geometry PG(m - 1, 2), there exist permutations π ∈ Sn, such that Hn and Hn do not have any Hamming subcode with the same support, or equivalently the corresponding projective geometries do not have any common flat. The introduced permutations are called AF permutations. We study some properties of these permutations and their relation with the well known APN functions. © 2011 Springer Science+Business Media, LLC.
Original languageEnglish
Pages (from-to)209-223
JournalDesigns, Codes, and Cryptography
Volume62
DOIs
Publication statusPublished - 1 Jan 2012

Keywords

  • APN functions
  • Cryptography
  • Hamming codes
  • Intersection of Hamming codes
  • Projective geometries

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