Codes over affine algebras with a finite commutative chain coefficient ring

@article{MartnezMoro2018CodesOA,
  title={Codes over affine algebras with a finite commutative chain coefficient ring},
  author={Edgar Mart{\'i}nez-Moro and Alejandro Pi{\~n}era-Nicol{\'a}s and Ignacio F. R{\'u}a},
  journal={Finite Fields and Their Applications},
  year={2018},
  volume={49},
  pages={94-107}
}
We consider codes defined over an affine algebra A = R[X1, . . . , Xr]/ 〈t1(X1), . . . , tr(Xr)〉, where ti(Xi) is a monic univariate polynomial over a finite commutative chain ring R. Namely, we study the A−submodules of A (l ∈ N). These codes generalize both the codes over finite quotients of polynomial rings and the multivariable codes over finite chain… CONTINUE READING