6 problems

Let $\mathcal{F}$ be a Ferrers diagram, let $C_{\mathcal{F}}$ be an FDRM code with minimum rank distance $\delta$, and let $\mathcal{C}_{\mathcal{F}}$ be the corresponding lifted F…

Let $q$ be a prime power, and let $B_q(v_1,v_2,d;k)$ denote the maximum size of a constant-dimension code in a $v_1$-dimensional vector space whose codewords have dimension $k$, mi…

Etzion's extension conjecture. The lower bound

Let ${\cal G}_q(n,k)$ denote the Grassmannian of $k$-dimensional subspaces of an $n$-dimensional vector space over $\mathbb{F}_q$. A code is $t$-intersecting if any two of its code…

Let $k=4$ and let $n$ be a power of two. Consider skeleton codes formed from codewords of weight $4$ in the extended Hamming code, with the columns of its parity-check matrix order…

Let $r$ be such that $n=2^{r}$, and consider the extended Hamming code with a parity-check matrix of the form similar to $(*)$. Take all codewords of weight $4$ and use them in the…