We construct an infinite family of commutative rings Rq,Δ and we study codes over these rings as well as the structure of the rings. We define a canonical Gray map from Rq,Δ to vectors over the residue finite field of q elements and use it to relate codes over Rq,Δ to codes over the finite field Fq. Finally, we determine the parameters for when self-dual codes exist and give various constructions for self-dual codes over Rq,Δ.
|Journal||Applicable Algebra in Engineering, Communications and Computing|
|Publication status||Accepted in press - 2020|
- Codes over rings
- Local rings
- Self-dual codes