Combining subspace codes
Antonio Cossidente, Sascha Kurz, Giuseppe Marino, Francesco Pavese, Mathematisches Institut, Universität Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany · Advances in Mathematics of Communications · 2021
In the context of constant-dimension subspace codes, an important problem is to determine the largest possible size $ A_q(n, d; k) $ of codes whose codewords are $ k $-subspaces of $ {\mathbb F}_q^n $ with minimum subspace distance $ d $. Here in order to obtain improved constructions, we investigate several approaches to combine subspace codes. This allow us to present improvements on the lower bounds for constant-dimension subspace codes for many parameters, including $ A_q(10, 4; 5) $, $ A_q(12, 4; 4) $, $ A_q(12, 6, 6) $ and $ A_q(16, 4; 4) $.