New LMRD code bounds for constant dimension codes and improved constructions

D. Heinlein

    Research output: Contribution to journalArticleScientificpeer-review

    9 Citations (Scopus)

    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 languageEnglish
    Article number8667306
    Pages (from-to)4822-4830
    Number of pages9
    JournalIEEE Transactions on Information Theory
    Volume65
    Issue number8
    Early online date2019
    DOIs
    Publication statusPublished - 1 Aug 2019
    MoE publication typeA1 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

    Fingerprint

    Dive into the research topics of 'New LMRD code bounds for constant dimension codes and improved constructions'. Together they form a unique fingerprint.

    Cite this