5 problems

Let $D=\Delta_{M_1}+\eta\Delta_{M_2}+\cdots+\eta^{n-1}\Delta_{M_n}\subset\mathbb{F}_{2^n}^m$ be as above, with the hypotheses stated in the source, and let $C^{(2)}_{D^c}$ be the a…

Let $D\subset\mathbb{F}_{2^n}^m$ be the defining set described above, and let $x=(x_1,\ldots,x_n)\in(\mathbb{F}_2^m)^n$. Write $c^{(2)}_{D^c}(x)$ and $c^{(2)}_{D^{\ast}}(x)$ for th…

Let $q=2^m$, with $m\equiv 3\pmod 4$ and $m\geq 5$, and define … Let ${\mathcal{C}}_{(f,q)}^{(2)}$ be the associated binary subfield code. Nine-weight conjecture. The code…

Let $q=2^m$, and let ${\mathcal{C}}_{(f,q)}^{(2)}$ be the binary subfield code defined by the trace representation for an oval polynomial $f$. Nine-weight conjecture. For odd…

Let $q=2^m$ and let ${\mathcal{C}}_{(x^3,q)}^{(2)}$ denote the binary subfield code considered in Theorem. Nine-weight conjecture. For odd $m\geq 5$, the code…