The construction of codes in the projective space for error control in random networks has been the focus of recent research. The Plücker coordinate description of subspaces has been discussed in the context of constant dimension codes, as well as the Schubert cell description of certain code parameters. In this paper we use this classical tool to reformulate some standard constructions of cons...

We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.

Some families of constant dimension codes arising from Riemann-Roch spaces associated to particular divisors of a curve X are constructed. These families are generalizations of the one constructed by Hansen [7].

Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of Fq with a given dimension. A computer search for large constant dimension codes is usually inefficient since the search space domain is extremely large. Even so, we found that some constant dimension lexicodes are larger than other...

Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional properties that can be applied efficiently in encoding and decoding algorithms. It is desirable to find cyclic constant dimension codes such that both the code ...

Constant dimension codes are subsets of the finite Grassmann variety. The study of constant dimension codes with good distances have been central in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are characterized that the elements of the code can be viewed as the orbit under a group action. The paper gives a complete characterization of ...

We introduce a new class of constant dimension codes called orbit codes. The basic properties of these codes are derived. It will be shown that many of the known families of constant dimension codes in the literature are actually orbit codes. DOI: https://doi.org/10.1109/CIG.2010.5592788 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh...

In this paper we construct constant dimension space codes with prescribed minimum distance. There is an increased interest in space codes since a paper [13] by Kötter and Kschischang were they gave an application in network coding. There is also a connection to the theory of designs over finite fields. We will modify a method of Braun, Kerber and Laue [7] which they used for the construction of...

An (r,M, 2δ; k)q constant–dimension subspace code, δ > 1, is a collection C of (k−1)–dimensional projective subspaces of PG(r−1, q) such that every (k−δ)–dimensional projective subspace of PG(r−1, q) is contained in at most a member of C. Constant–dimension subspace codes gained recently lot of interest due to the work by Koetter and Kschischang [18], where they presented an application of such...

We investigate subspace codes whose codewords are subspaces of PG(4, q) having non– constant dimension. In particular, examples of optimal mixed–dimension subspace codes are provided, showing that Aq(5, 3) = 2(q 3 + 1).