Equidistant Codes in the Grassmannian

Abstract

Equidistant codes over vector spaces are considered. For $k$-dimensional subspaces over a large vector space the largest code is always a sunflower. We present several simple constructions for such codes which might produce the largest non-sunflower codes. A novel construction, based on the Plücker embedding, for 1-intersecting codes of $k$-dimensional subspaces over $\F_q^n$, $n\ge \left(\genfrac{}{}{0ex}{}{k+1}{2}\right)$, where the code size is $\frac{q^{k+1}-1}{q-1}$ is presented. Finally, we present a related construction which generates equidistant constant rank codes with matrices of size $n\times \left(\genfrac{}{}{0ex}{}{n}{2}\right)$ over $\F_q$, rank $n-1$, and rank distance $n-1$.

16 pages

References in corpus (4)

• A Rank-Metric Approach to Error Control in Random Network Coding
• Forms and Linear Network Codes
• Decoding of Subspace Codes, a Problem of Schubert Calculus over Finite Fields
• Osculating Spaces of Varieties and Linear Network Codes

Cited by in corpus (1)

• Distributed Storage Systems based on Equidistant Subspace Codes