Hyperplane Sections of Grassmannians and the Number of MDS Linear Codes

Authors: Ghorpade S.R.1; Lachaud G.2

Source: Finite Fields and Their Applications, Volume 7, Number 4, October 2001 , pp. 468-506(39)

Publisher: Academic Press

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content

Abstract:

We obtain some effective lower and upper bounds for the number of (n,k)-MDS linear codes over Fopfq. As a consequence, one obtains an asymptotic formula for this number. These results also apply for the number of inequivalent representations over Fopfq of the uniform matroid or, alternately, the number of Fopfq-rational points of certain open strata of Grassmannians. The techniques used in the determination of bounds for the number of MDS codes are applied to deduce several geometric properties of certain sections of Grassmannians by coordinate hyperplanes. Copyright 2001 Academic Press.

Keywords: Grassmannians; MDS codes; hyperplane sections; uniform matroids; arcs in projective spaces

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, Indian Institute of Technology, Bombay, Powai, Mumbai, 400076, India 2: Institut de Mathématiques de Luminy, Luminy Case 907, Marseille, Cedex 9, 13288, France

The full text electronic article is available for purchase. You will be able to download the full text electronic article after payment.

$54.13 plus tax      Refund Policy

 

OR

Back to top

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content
Share this item with others: These icons link to social bookmarking sites where readers can share and discover new web pages.
Page Help Click here for Page Help
Shopping cart
Tools
Sign in






Need to register?
Sign up here
Text size: A | A | A | A