Author/Authors :
irwansyah, . universitas mataram - department of mathematics, Mataram, Indonesia , irwansyah, . institut teknologi bandung - algebra research group, Bandung, Indonesia , muchtadi-alamsyah, intan institut teknologi bandung - algebra research group, Bandung, Indonesia , muchlis, ahmad institut teknologi bandung - algebra research group, Bandung, Indonesia , barra, aleams institut teknologi bandung - algebra research group, Bandung, Indonesia , suprijanto, djoko institut teknologi bandung - combinatorial research group, Bandung, Indonesia
Abstract :
In this paper, we will show some properties of codes over the ring Bk = Fp[v1; : : : ; vk]=(v^2i = vi; 8i = 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 Bk. Then, we define certain Gray map which can be used to give a connection between codes over Bk and codes over Fp. Using the previous connection, we give a characterization for equivalence of codes over Bk and Euclidean self-dual codes. Furthermore, we give generators for invariant ring of Euclidean self-dual codes over Bk through MacWilliams relation of Hamming weight enumerator for such codes.
Keywords :
Gray map , Equivalence of codes , Euclidean self , dual , Hamming weight enumerator , MacWilliams relation , Invariant ring
