Linear codes over ℤ4[x]/⟨x² + 2x⟩
by Edgar Martínez-Moro; Steve Szabo; Bahattin Yildiz
International Journal of Information and Coding Theory (IJICOT), Vol. 3, No. 1, 2015

Abstract: 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.

Online publication date: Thu, 09-Apr-2015

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