An improvement of the Johnson bound for subspace codes

نویسندگان

  • Michael Kiermaier
  • Sascha Kurz
چکیده

Subspace codes, i.e., subset of a finite-field Grassmannian, are applied in random linear network coding. Here we give improved upper bounds based on the Johnson bound and a connection to divisible codes, which is presented in a purely geometrical way. This complements a recent approach for upper bounds on the maximum size of partial spreads based on projective qr-divisible codes.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Isotropic Constant Dimension Subspace Codes

 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...

متن کامل

On the extendability of particular classes of constant dimension codes

In classical coding theory, different types of extendability results of codes are known. A classical example is the result stating that every (4, q − 1, 3)-code over an alphabet of order q is extendable to a (4, q, 3)-code. A constant dimension subspace code is a set of (k− 1)-spaces in the projective space PG(n− 1, q), which pairwise intersect in subspaces of dimension upper bounded by a speci...

متن کامل

Geometric constructions of optimal optical orthogonal codes

We provide a variety of constructions of (n,w, λ)-optical orthogonal codes using special sets of points and Singer groups in finite projective spaces. In several of the constructions, we are able to prove that the resulting codes are optimal with respect to the Johnson bound. The optimal codes exhibited have λ = 1, 2 and w − 1 (where w is the weight of each codeword in the code). The remaining ...

متن کامل

Cyclic Orbit Codes with the Normalizer of a Singer Subgroup

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

متن کامل

A Singleton Bound for Lattice Schemes

The binary coding theory and subspace codes for random network coding exhibit similar structures. The method used to obtain a Singleton bound for subspace codes mimic the technique used in obtaining the Singleton bound for binary codes. This motivates the question of whether there is an abstract framework that captures these similarities. As a first step towards answering this question, we use ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • CoRR

دوره abs/1707.00650  شماره 

صفحات  -

تاریخ انتشار 2017