Codes over an infinite family of algebras

Irwansyah, Intan Muchtadi-Alamsyah, Ahmad Muchlis, Aleams Barra, Djoko Suprijanto
2017 Journal of Algebra Combinatorics Discrete Structures and Applications  
In this paper, we will show some properties of codes over the ring B k = Fp[v1, . . . , v k ]/(v 2 i = vi, ∀i = 1, . . . , k). These rings, form a family of commutative algebras over finite field Fp. 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 Fp. Using the previous connection, we give a characterization for equivalence of
more » ... or 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. 2010 MSC: 11T71
doi:10.13069/jacodesmath.284947 fatcat:bfc65eeharajfbp56c55nywjz4