Karthik Sheshadri

Trellis State Complexity as an Exact Tropical Factorization Rank

Let $C\subseteq\F_2^m$ be a binary linear code and let $[m]=L\sqcup R$ be a bipartition of its coordinates. The \emph{conditional decoding matrix} of $C$ at this cut is the matrix $W$ indexed by $\F_2^{L}\times\F_2^{R}$ whose entry $W(x_L,x_R)$ is the coset-leader weight $d\bigl((x_L,x_R),C\bigr)$, the minimum Hamming...