Subject: Q Science (General)
Year: 2019
Type: Article
Type: PeerReviewed
Title: FINITE PROJECTIVE PLANES AND HAMMING CODES
Author: Sadiki, Flamure
Abstract: This paper is a short survey of projective geometry, history of Hamming codes and the relationship between them and projective planes. The projective plane of order , over a finite field , which has arithmetic done , denoted by , is the set of all subspaces of vector space . It can be endowed with the distance function , which turns into a metric space. A code in projective space is a subset of of size such that the distance between any two code-words is at least . The first error correction code, the Hamming code, is intrinsic to the projective plane of order 2 over . A connection between planes and codes is given by construction of Hamming code related to and we generalize them to using Hamming and Generator matrix. The codes constructed in this way are called projective codes.
Publisher: Faculty of Natural Sciences and Mathematics - University of Tetova
Relation: https://eprints.unite.edu.mk/457/
Identifier: oai:eprints.unite.edu.mk:457
Identifier: https://eprints.unite.edu.mk/457/1/28.pdfIdentifier: Sadiki, Flamure (2019) FINITE PROJECTIVE PLANES AND HAMMING CODES. Journal of Natural Sciences and Mathematics of UT, 4 (7-8). pp. 211-217. ISSN 2671-3039
