A Note on Constacyclic and Quasi-cyclic Codes over F2+ uF2+ vF2+ uvF2

Abstract

In this paper, we study (1 + λu) -constacyclic codes of length 2 k over the ring R = F2+ uF2+ vF2+ uvF2, where u2=v2=0,uv=vu, k is a positive integer and λ is a unit in R. We classify all (1 + λu) -constacyclic codes of length 2 k over R. We also completely classify the structure of (1 + λu) -constacyclic codes of length 2 k over R that are contained in their annihilators as well as equal to their annihilators. We enumerate these codes and present mass formulas for them. Some optimal codes are obtained as the Gray images of these codes. In addition, we also study the structure of 1-generator generalized quasi-cyclic codes over the ring R. A minimal spanning set for these codes is determined. A BCH-type bound on the minimum distance of these codes is also presented. © 2019, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.