64 research outputs found
Codes and Designs Related to Lifted MRD Codes
Lifted maximum rank distance (MRD) codes, which are constant dimension codes,
are considered. It is shown that a lifted MRD code can be represented in such a
way that it forms a block design known as a transversal design. A slightly
different representation of this design makes it similar to a analog of a
transversal design. The structure of these designs is used to obtain upper
bounds on the sizes of constant dimension codes which contain a lifted MRD
code. Codes which attain these bounds are constructed. These codes are the
largest known codes for the given parameters. These transversal designs can be
also used to derive a new family of linear codes in the Hamming space. Bounds
on the minimum distance and the dimension of such codes are given.Comment: Submitted to IEEE Transactions on Information Theory. The material in
this paper was presented in part in the 2011 IEEE International Symposium on
Information Theory, Saint Petersburg, Russia, August 201
Message Encoding for Spread and Orbit Codes
Spread codes and orbit codes are special families of constant dimension
subspace codes. These codes have been well-studied for their error correction
capability and transmission rate, but the question of how to encode messages
has not been investigated. In this work we show how the message space can be
chosen for a given code and how message en- and decoding can be done.Comment: Submitted to IEEE International Symposium on Information Theory 201
Optimal Binary Locally Repairable Codes via Anticodes
This paper presents a construction for several families of optimal binary
locally repairable codes (LRCs) with small locality (2 and 3). This
construction is based on various anticodes. It provides binary LRCs which
attain the Cadambe-Mazumdar bound. Moreover, most of these codes are optimal
with respect to the Griesmer bound
Subspaces intersecting in at most a point
We improve on the lower bound of the maximum number of planes in
\operatorname{PG}(8,q)\cong\F_q^{9} pairwise intersecting in at most a point.
In terms of constant dimension codes this leads to . This result is obtained via a more general
construction strategy, which also yields other improvements.Comment: 4 page
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