Narrow Results

We take a Galois ring $GR(p^m,g)$ and discuss about the self-dual codes and its properties over the ring. We will also describe the relationship between Clifford-Weil group and Jacobi forms by constructing the invariant polynomial ring with the complete weight enumerator.

In this paper, we showed that any clone of operations preserving a nontrivial $n$-equivalence on a finite set is categorically equivalent to the clone of operations preserving a nontrivial $n$-equivalence on a set having the cardinality of $3$.

In this paper, we consider an imaginary quadratic field $K=\mathbb{Q}(\sqrt{-m})$ with $-m\equiv 3$ (mod $4$). In particular, we study the ring of integers corresponding to the field $K$ and visualize the form of ${𝜖}_K/p{𝜖}_K$. We also consider lattices over the ring of integers ${𝜖}_K$ and discuss the theta series to see its relation with the weight enumerator. As a consequence, we will see how the theta series differs for different $m$ and $m^{\prime }$.