@article{article_284947, title={Codes over an infinite family of algebras}, journal={Journal of Algebra Combinatorics Discrete Structures and Applications}, volume={4}, pages={131–140}, year={2017}, DOI={10.13069/jacodesmath.284947}, author={Irwansyah, - and Muchtadi-alamsyah, İntan and Muchlis, Ahmad and Barra, Aleams and Suprijanto, Djoko}, keywords={Gray map,Equivalence of codes,Euclidean self-dual,Hamming weight enumerator,MacWilliams relation,Invariant ring}, abstract={In this paper, we will show some properties of codes over the ring $B_k=\mathbb{F}_p[v_1,\dots,v_k]/(v_i^2=v_i,\forall i=1,\dots,k).$ These rings, form a family of commutative algebras over finite field $\mathbb{F}_p$. We first discuss about the form of maximal ideals and characterization of automorphisms for the ring $B_k$. Then, we define certain Gray map which can be used to give a connection between codes over $B_k$ and codes over $\mathbb{F}_p$. Using the previous connection, we give a characterization for equivalence of codes over $B_k$ and Euclidean self-dual codes. Furthermore, we give generators for invariant ring of Euclidean self-dual codes over $B_k$ through MacWilliams relation of Hamming weight enumerator for such codes.}, number={2 (Special Issue: Noncommutative rings and their applications)}, publisher={iPeak Academy}