7 problems

Existence conjecture. There exists a cyclic subspace code $\mathcal{C}\subseteq \mathcal{G}_q(n,k)$ such that

Let $\mathbb{P}_2(n)$ be the projective space consisting of the subspaces of $\mathbb{F}_2^n$, and let a linear code be a subset of $\mathbb{P}_2(n)$ endowed with the linear struct…

Let $\mathcal{U}$ be a linear code in the projective space $\mathbb{P}_q(n)$. An indecomposable basis is a basis of the vector space over $\mathbb{F}_2$ formed by the code whose el…

Let $\mathbb{P}_q(n)$ be the projective space of subspaces of $\mathbb{F}_q^n$, equipped with the notion of linear code introduced by Braun, Etzion, and Vardy. The BEV bound states…

Cyclic subspace code existence conjecture. There exists a cyclic subspace code

RRP bound conjecture. For any packet length $v\geq 7$ with $v\notin\{8,10\}$, the largest subspace codes that can be obtained by solving the RRP exceed the LMRD code bound and thus…

Let $\mathcal{G}_{q}(n,k)$ denote the Grassmannian of $k$-dimensional subspaces of $\mathbb{F}_{q}^{n}$, and let a cyclic code be a subspace code invariant under multiplication by…