New LMRD Code Bounds for Constant Dimension Codes and Improved Constructions
Daniel Heinlein · IEEE Transactions on Information Theory · 2019
We prove upper bounds for the cardinality of constant dimension codes (CDC) which contain a lifted maximum rank distance (LMRD) code as a 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 the new largest and sometimes bound achieving CDCs for small parameters.