4 problems

Let $R$ be a commutative finite chain ring (CFCR) of nilpotency index $e$, and let $n$ be a positive integer. Let $C_n(R)$ denote the ring of $n\times n$ circulant matrices over…

Let $R$ be a commutative finite chain ring (CFCR) of nilpotency index $e$, let $n$ be a positive integer, and suppose that the maximal ideal of $R$ is generated by $gamma$. Write…

Kumar's conjecture. Every convolutional code over $\mathbb Z_{p^r}$ admits a noncatastrophic $p$-encoder. Noncatastrophic $p$-encoders provide a useful encoder-level finiteness pro…

Let $\mathcal{C}$ be an extended $Z_{2^m}$-quadratic residue code, and let a punctured code be obtained from $\mathcal{C}$ by deleting one coordinate. Punctured extended quadratic…