6 problems

Let $\mathbf{H}=\mathbf{H}_{\operatorname{PG}(2,q)}$. Consider minimal pseudo-codewords having minimum AWGNC pseudo-weight among all minimal pseudo-codewords that are not multiples…

Let $q$ be an even prime power and let $\mathbf{H}=\mathbf{H}_{\operatorname{PG}(2,q)}$. A component is significant if, for most lines passing through its point, its value is the s…

Consider the construction described in the preceding examples: start with minimal codewords or pseudo-codewords, add them, and modify selected low-valued components to obtain a min…

Let $\mathbf{H}=\mathbf{H}_{\operatorname{PG}(2,q)}$ and let $\boldsymbol{\omega}\in\mathcal{K}(\mathbf{H})$ be a minimal pseudo-codeword of type $\mathbf{t}$, where $t_0$ is non-n…

Let $d_c>d_v\geq 3$ be integers satisfying $d_v<\beta_{d_c}d_c$, where $\beta_{d_c}$ is Calkin's threshold. For a positive constant $\lambda$, let $\Gamma_{\lambda}$ be the ensembl…

Let $d_v$ and $d_c$ be integers with $d_c>d_v\geq 3$. A Tanner graph is asymptotically strong if, for every constant $\beta>0$, there is a constant $\alpha>0$ such that its LP deco…