Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects

Abstract

In this article, the partial plane spreads in $PG(6,2)$ of maximum possible size $17$ and of size $16$ are classified. Based on this result, we obtain the classification of the following closely related combinatorial objects: Vector space partitions of $PG(6,2)$ of type $(3^{16}{4}^1)$, binary $3\times 4$ MRD codes of minimum rank distance $3$, and subspace codes with parameters $(7,17,6{)}_2$ and $(7,34,5{)}_2$.

31 pages, 9 tables

References in corpus (8)

• Tables of subspace codes
• Coset Construction for Subspace Codes
• Algebraic structures of MRD Codes
• Partial spreads and vector space partitions
• New Criteria for MRD and Gabidulin Codes and some Rank-Metric Code Constructions
• Improved upper bounds for partial spreads
• Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6
• New LMRD bounds for constant dimension codes and improved constructions

Cited by in corpus (5)

• Tables of subspace codes
• Projective divisible binary codes
• Affine vector space partitions
• On projective $q^r$-divisible codes
• Binary additive MRD codes with minimum distance n-1 must contain a semifield spread set