4 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…

Type conjecture. The type $\boldsymbol{t}$ of these pseudo-codewords has $t_0$ non-negative, $t_1$ positive, $t_2$ positive, and $t_\ell=0$ otherwise. If this is false, the smalles…

Structural conjecture. Every minimal pseudo-codeword is a sum of a few minimal pseudo-codewords, with one or two low-value components changed so that they become the large componen…