Time: 9h, Wednesday, August 7, 2019,
Location: Room 507, Building A6, Institute of Mathematics
Abstract: Unlike the simple-root case, it is shown that the ambient rings of repeated-root constacyclic codes over finite chain rings are usually not principal ideal rings. We discuss the algebraic structure of repeated-root $\lambda$-constacyclic codes of prime power length $p^s$ over any finite commutative chain ring $R$. It is proven that the ambient ring $\frac{R[x]}{\langle x^{p^s}-\lambda \rangle}$ is a local ring with maximal ideal $\langle x-\lambda, \gamma \rangle$. Among other things, the nilpotency indices of $x-1$ and $x+1$ in the ambient rings $\frac{R[x]}{\langle x^{p^s}-1 \rangle}$ and $\frac{R[x]}{\langle x^{p^s}+1 \rangle}$, respectively, are established. We will also discuss some special cases of the chain ring $R$ that were studied in the literature, as well as some generalizations on the lengths and alphabets of the codes.