Intersection of Hadamard codes

Kevin T. Phelps, Mercè Villanueva

    Research output: Contribution to journalArticleResearchpeer-review

    3 Citations (Scopus)

    Abstract

    For two binary codes C1,C2, define i (C1, C2)= C1 ∩ C2 to be their intersection number. This correspondence establishes that there exist Hadamard codes of length 2t, for all t ≥ 3, with intersection number i if and only if i ∈ {0,2,4,..., 2t+1 - 12, 2t+1 - 8, 2t+1}. Also it is proved that for all t ≥ 4, if there exists a Hadamard matrix of order 4s, then there exist Hadamard codes of length 2t+2s with intersection number i if and only if i ∈ {0,2,4,..., 2t+3s - 12, 2t+3s - 8, 2t+3s}. © 2007 IEEE.
    Original languageEnglish
    Pages (from-to)1924-1928
    JournalIEEE Transactions on Information Theory
    Volume53
    DOIs
    Publication statusPublished - 1 May 2007

    Keywords

    • Extended Hamming codes
    • Hadamard codes
    • Hadamard designs
    • Hadamard matrices
    • Intersection number

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