Linear codes over Z4[x]/{x2+2x}

  1. Moro, Edgar Martínez 2
  2. Szabo, Steve 3
  3. Yildiz, Bahattin 1
  1. 1 Fatih University
    info

    Fatih University

    Estambul, Turquía

    ROR https://ror.org/02wbrth70

  2. 2 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

  3. 3 Eastern Kentucky University
    info

    Eastern Kentucky University

    Richmond, Estados Unidos

    ROR https://ror.org/012xks909

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Zeitschrift:
International Journal of Information and Coding Theory

ISSN: 1753-7703,  1753-7711

Datum der Publikation: 2015

Ausgabe: 3

Nummer: 1

Seiten: 78

Art: Artikel

DOI: 10.1504/IJICOT.2015.068698 GOOGLE SCHOLAR lock_openOpen Access editor

Andere Publikationen in: International Journal of Information and Coding Theory

Zusammenfassung

In this work codes over one of seven local Frobenius non–chain rings of order 16 are studied. The ring structure is discussed showing both the similarities and differences to a previously studied ring. A duality preserving Gray map is given and is used to present MacWilliams identities and self–dual codes. Connections between these self–dual codes and real unimodular lattices are also discussed. Some extremal Type II ℤ4–codes are provided as images of codes over this ring. ℤ4–codes that are images of linear codes over the studied ring are characterised through automorphism groups and some well–known families of ℤ4–codes (different versions of quaternary Reed–Muller codes) are proved to be linear over it.