NDLI: Higher distances for constant dimensions codes: the case of osculating spaces to a Veronese variety

Please wait, while we are loading the content...

Afrika Matematika : Volume 28

Afrika Matematika : Volume 27

Afrika Matematika : Volume 27, Issue 7-8, December 2016

Afrika Matematika : Volume 27, Issue 5-6, September 2016

Fixed point theorems for $$\alpha $$ -integral type G-contraction mappings

Efficient families of Newton’s method and its variants suitable for non-convergent cases

On certain Toeplitz matrices via difference operator and their applications

Existence of solutions for a class of obstacle problems with $$L^1$$ -data and without sign condition

An iterative method for solving singular linear systems with index one

A hybrid class of expansive-contractive mappings in cone b-metric spaces

Ostrowski type Inequalities for m- and $$\left( \alpha ,m\right) $$ -geometrically convex functions via Riemann–Louville Fractional integrals

The rational homotopy type of elliptic spaces up to cohomological dimension 8

A family of higher order multi-point iterative methods based on power mean for solving nonlinear equations

A class of Boehmians for a recent generalization of Hankel–Clifford transformation of arbitrary order

Fekete–Szegö problem for certain classes of Ma-Minda bi-univalent functions

Presenting degenerate Ringel–Hall Algebras of type $$E_6$$

Existence of a variational solution for the stationary Boussinesq equations with thermocapillary effect and nonhomogenous boundary conditions

Starlike functions associated with a cardioid

A power of a meromorphic function sharing a set with its derivative

Approximating a common fixed point of finite family of asymptotically quasi-nonexpansive mappings in Banach spaces

Second derivative of high-order accuracy methods for the numerical integration of stiff initial value problems

On certain missing links in the hierarchy of some compact-like covering properties

On partially included intuitionistic fuzzy rough relations

Higher distances for constant dimensions codes: the case of osculating spaces to a Veronese variety

A unified study on starlike and convex functions associated with Poisson distribution series

An Harnack inequality for the quasi-minima of scalar integral functionals with nearly linear growth conditions

Les m-derivations des algebres de Lie de champs de vecteurs polynomiaux

Relation d’équivalence sur les algèbres quasi-Batalin–Vilkovisky différentielles

Spectral theorems associated with the Cherednik operators on $$\mathbb {R}^{d}$$

Afrika Matematika : Volume 27, Issue 3-4, June 2016

Afrika Matematika : Volume 27, Issue 1-2, March 2016

Afrika Matematika : Volume 26

Afrika Matematika : Volume 25

Afrika Matematika : Volume 24

Afrika Matematika : Volume 23

Afrika Matematika : Volume 22

Higher distances for constant dimensions codes: the case of osculating spaces to a Veronese variety

Content Provider	Springer Nature Link
Author	Ballico, Edoardo
Copyright Year	2016
Abstract	In linear network coding the information is encoded in terms of a basis of a vector space and it is received as a basis of a possible altered vector space. In the constant dimension case Koetter and Kschischang introduced a metric on the Grassmannian and proved efficient and correct decoding in terms of this metric. Here we introduce a second order invariant of the code: the minimum dimension of the linear span of 3 different linear subspaces belonging to the code. This is the case $$s=3$$ of a family $$d_s$$ and $$d'_s$$ , $$s\ge 3$$ , of invariants of network codes. We study these invariants in a case recently proposed by Hansen (the set of all osculating spaces of a Veronese embedding of a finite projective space) and for a related case (the set of osculating spaces to curves of positive genus) with a complete description of the case of elliptic curves and the ones related to the Hermitian curve.
Starting Page	1003
Ending Page	1020
Page Count	18
File Format	PDF
ISSN	10129405
Journal	Afrika Matematika
Volume Number	27
Issue Number	5-6
e-ISSN	21907668
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-02-13
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Linear network coding Grassmannian Osculating space Generalized Hamming weight Constant dimension linear network coding Veronese embedding Elliptic curve Hermitian curve Geometric methods Projective techniques Mathematics Applications of Mathematics History of Mathematical Sciences Mathematics Education
Content Type	Text
Resource Type	Article
Subject	Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

The Weight Hierarchy of Hermitian Codes

Relative Generalized Rank Weight of Linear Codes and Its Applications to Network Coding

The second generalized Hamming weight for two-point codes on a Hermitian curve

Relative Generalized Hamming Weights of One-Point Algebraic Geometric Codes

A complete characterization of irreducible cyclic orbit codes and their Plücker embedding

A Terracini Lemma for osculating spaces with applications to Veronese surfaces

Generalized Hamming weights of codes obtained from smooth plane curves

Any network code comes from an algebraic curve taking osculating spaces

Any network codes comes from an algebraic curve taking osculating spaces

Higher distances for constant dimensions codes: the case of osculating spaces to a Veronese variety

Similar Documents

The Weight Hierarchy of Hermitian Codes

Relative Generalized Rank Weight of Linear Codes and Its Applications to Network Coding

The second generalized Hamming weight for two-point codes on a Hermitian curve

Relative Generalized Hamming Weights of One-Point Algebraic Geometric Codes

A complete characterization of irreducible cyclic orbit codes and their Plücker embedding

A Terracini Lemma for osculating spaces with applications to Veronese surfaces

Generalized Hamming weights of codes obtained from smooth plane curves

Any network code comes from an algebraic curve taking osculating spaces

Any network codes comes from an algebraic curve taking osculating spaces

Higher distances for constant dimensions codes: the case of osculating spaces to a Veronese variety