Grassmannian codes as lifts of matrix codes derived as images of linear block codes over finite fields

Issue Date

4-2016

Abstract

Let p be a prime such that p≡2 or 3 mod 5. Linear block codes over the non-commutative matrix ring of 2×2 matrices over the prime field GF(p) endowed with the Bachoc weight are derived as isometric images of linear block codes over the Galois field GF(p2) endowed with the Hamming metric. When seen as rank metric codes, this family of matrix codes satisfies the Singleton bound and thus are maximum rank distance codes, which are then lifted to form a special class of subspace codes, the Grassmannian codes, that meet the anticode bound. These so-called anticode-optimal Grassmannian codes are associated in some way with complete graphs. New examples of these maximum rank distance codes and anticode-optimal Grassmannian codes are given. Finally, examples of subspace codes which are not Grassmannian are given which are obtained from the anticode-optimal Grassmannian codes.

Source or Periodical Title

Global Journal of Pure and Applied Mathematics

ISSN

0973-1768

Volume

12

Issue

2

Page

1801-1820

Document Type

Article

Physical Description

tables

Language

English

Subject

Grassmannian codes, Maximum rank distance codes, Network coding, Subspace codes

Digital Copy

yes

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