Some new binary quasi-cyclic codes from codes over the ring $$\mathbb F _2+u\mathbb F _2+v\mathbb F _2+uv\mathbb F _2$$ F 2 + u F 2 + v F 2 + u v F 2

Abstract

We consider quasi-cyclic codes over the ring \(\mathbb{F }_2+u\mathbb{F }_2+v\mathbb{F }_2+uv\mathbb{F }_2\), a finite non-chain ring that has been recently studied in coding theory. The Gray images of these codes are shown to be binary quasi-cyclic codes. Using this method we have obtained seventeen new binary quasi-cyclic codes that are new additions to the database of binary quasi-cyclic codes. Moreover, we also obtain a number of binary quasi-cyclic codes with the same parameters as best known binary linear codes that otherwise have more complicated constructions.