TL;DR
This paper classifies equidistant subspace codes, showing they are mostly sunflowers or their orthogonals, and introduces a construction and decoding algorithm for such codes.
Contribution
It provides a near-complete classification of equidistant subspace codes and introduces a systematic construction and decoding method.
Findings
Most maximum equidistant codes are sunflowers or their orthogonals.
A systematic construction for equidistant codes is proposed.
An efficient decoding algorithm for these codes is developed.
Abstract
In this paper we study equidistant subspace codes, i.e. subspace codes with the property that each two distinct codewords have the same distance. We provide an almost complete classification of such codes under the assumption that the cardinality of the ground field is large enough. More precisely, we prove that for most values of the parameters, an equidistant code of maximum cardinality is either a sunflower or the orthogonal of a sunflower. We also study equidistant codes with extremal parameters, and establish general properties of equidistant codes that are not sunflowers. Finally, we propose a systematic construction of equidistant codes based on our previous construction of partial spread codes, and provide an efficient decoding algorithm.
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