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Abstract
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 language | English |
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Article number | 8667306 |
Pages (from-to) | 4822-4830 |
Number of pages | 9 |
Journal | IEEE Transactions on Information Theory |
Volume | 65 |
Issue number | 8 |
Early online date | 2019 |
DOIs | |
Publication status | Published - 1 Aug 2019 |
MoE publication type | A1 Journal article-refereed |
Keywords
- 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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Dive into the research topics of 'New LMRD code bounds for constant dimension codes and improved constructions'. Together they form a unique fingerprint.Projects
- 1 Finished
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Construction and Classification of Discrete Mathematic Structures
Östergård, P. (Principal investigator)
01/09/2015 → 31/08/2019
Project: Academy of Finland: Other research funding