FINITE PROJECTIVE PLANES AND HAMMING CODES

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

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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.

Item Type:	Article
Subjects:	Q Science > Q Science (General)
Divisions:	Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User:	Unnamed user with email zshi@unite.edu.mk
Date Deposited:	22 Feb 2020 18:41
Last Modified:	22 Feb 2020 18:41
URI:	http://eprints.unite.edu.mk/id/eprint/457

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