Isotropic Constant Dimension Subspace Codes

Authors

  • S. R. Adhami
Abstract:

 In network code setting, a constant dimension code is a set of k-dimensional subspaces of F nq . If F_q n is a nondegenerated symlectic vector space with bilinear form f, an isotropic subspace U of F n q is a subspace that for all x, y ∈ U, f(x, y) = 0. We introduce isotropic subspace codes simply as a set of isotropic subspaces and show how the isotropic property use in decoding process, then we show that for suitable parameters there are isotropic spread codes.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Isometry and automorphisms of constant dimension codes

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.

full text

Constant dimension codes from Riemann-Roch spaces

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].

full text

Large constant dimension codes and lexicodes

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...

full text

Constructions of cyclic constant dimension codes

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 ...

full text

Johnson type bounds on constant dimension codes

Very recently, an operator channel was defined by Koetter and Kschischang when they studied random network coding. They also introduced constant dimension codes and demonstrated that these codes can be employed to correct errors and/or erasures over the operator channel. Constant dimension codes are equivalent to the so-called linear authentication codes introduced by Wang, Xing and Safavi-Nain...

full text

Constructions and bounds for mixed-dimension subspace codes

Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. The resulting so-called Main Problem of Subspace Coding is to determine the maximum size Aq(v, d) of a code in PG(v−1,Fq) with minimum subspace distance d. Here we completely resolve this problem for d ≥ v − 1. For d = v − 2 we present some improved bounds ...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 14  issue 1

pages  21- 34

publication date 2019-04

By following a journal you will be notified via email when a new issue of this journal is published.

Keywords

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023