On ℤ4-Linear Preparata-Like and Kerdock-Like Codes

Joaquim Borges, Kevin T. Phelps, Josep Rifà, Victor A. Zinoviev

    Research output: Contribution to journalArticleResearchpeer-review

    17 Citations (Scopus)

    Abstract

    We say that a binary code of length n is additive if it is isomorphic to a subgroup of ℤ2α × ℤ4β, where the quaternary coordinates are transformed to binary by means of the usual Gray map and hence α + 2β = n. In this paper, we prove that any additive extended Preparata-like code always verifies α = 0, i.e., it is always a ℤ4-linear code. Moreover, we compute the rank and the dimension of the kernel of such Preparata-like codes and also the rank and the kernel of the ℤ4-dual of these codes, i.e., the ℤ4 -linear Kerdock-like codes.
    Original languageEnglish
    Pages (from-to)2834-2843
    JournalIEEE Transactions on Information Theory
    Volume49
    DOIs
    Publication statusPublished - 1 Nov 2003

    Keywords

    • Additive codes
    • Kerdock code
    • Kernel
    • Preparata code
    • Rank
    • ℤ -linear codes 4

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