LCD subspace codes

Dean Crnkovic, Andrea Svob

Published 2022-04-18Version 1

A subspace code is a nonempty set of subspaces of vectors space $\mathbb F^n_q$. Linear codes with complementary duals, or LCD codes, are linear codes whose intersection with their duals are trivial. In this paper, we introduce a notion of LCD subspace codes. We show that the nearest-codeword (or maximum-likelihood) decoding problem for an LCD subspace code reduces to a problem that is simpler than for a general subspace code. Further, we show that under some conditions equitable partitions of association schemes yield such LCD subspace codes and as an illustration of the method give some examples from distance-regular graphs.