Cyclic codes over M4(F2 + uF2) (Mar, 10.1007/s12095-022-00572-9, 2022)

Let p be a prime and Fq be a finite field for q= pm. In this paper, we consider the ring R= M4(F2+ uF2) of 4 × 4 matrices over the finite ring F2+ uF2 with u2= 0. Then R is a noncommutative non-chain ring of cardinality 4 16 and isomorphic to the ring F16+ vF16+ v2F16+ v3F16+ uF16+ uvF16+ uv2F16+ uv3F16, where v4= 0 , uv= vu, uv2= v2u and uv3= v3u. Here, first we establish the structure of cyclic codes and their generators over R and later the dual (Euclidean and Hermitian both) of these cyclic codes are discussed. Further, with the help of the Gray map, we show that the image of a cyclic code is an F16-linear code. Finally, we provide some non-trivial examples of linear codes with good parameters to support our derived results. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.