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.
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