New LMRD code bounds for constant dimension codes and improved constructions

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We prove upper bounds for the cardinality of constant dimension codes (CDC) which contain a lifted maximum rank distance code (LMRD code) as subset. Thereby we cover all parameters fulfilling k < 3d=2, where k is the codeword dimension and d is the minimum subspace distance. The proofs of the bounds additionally show that an LMRD code L can be unioned with a CDC C (of fitting parameters) without violating the subspace distance condition iff each codeword of C intersects the special subspace of L in at least dimension d=2. This connection is used to find new largest and sometimes bound achieving CDCs for small parameters.
Original languageEnglish
Article number8667306
Pages (from-to)4822-4830
Number of pages9
JournalIEEE Transactions on Information Theory
Issue number8
Early online date2019
Publication statusPublished - 1 Aug 2019
MoE publication typeA1 Journal article-refereed


  • Upper bound
  • Finite element analysis
  • Indexes
  • Extraterrestrial measurements
  • Encoding
  • Finite projective spaces
  • constant dimension codes
  • subspace codes
  • subspace distance
  • rank distance
  • maximum rank distance codes
  • lifted maximum rank distance code bound
  • combinatorics

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