Open AccessApplications of the Projective Plane in Coding Theory
Author(s) -
Najm Abdulzahra Makhrib Al-Seraji,
Zainab Sadiq Jafar
Publication year - 2020
Publication title -
xi'nan jiaotong daxue xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 21
ISSN - 0258-2724
DOI - 10.35741/issn.0258-2724.55.1.2
Subject(s) - coding theory , projective plane , coding (social sciences) , finite geometry , mathematics , projective test , dimension (graph theory) , finite field , code (set theory) , projective space , discrete mathematics , pure mathematics , computer science , combinatorics , geometry , programming language , statistics , set (abstract data type) , correlation
The goal of this paper was to study the applications of the projective plane PG (2, q) over a Galois field of order q in the projective linear (n, k, d, q) -code such that the parameters length of code n, the dimension of code k, and the minimum distance d with the error-correcting e according to an incidence matrix have been calculated. Also, this research provides examples and theorems of links between the combinatorial structures and coding theory. The calculations depend on the GAP (groups, algorithms, and programming) system. The method of the research depends on the classification of the points and lines in PG (2, q).