Applications of the Projective Space PG (3,8) in Coding Theory

Abstract

The main objective of this research is to present the relationship between the subject of coding theory and three-dimensional projection space in the eighth field. We found the points, lines, and planes of the Galois field of order 8 using algebraic equations. Then, we formed a projective matrix with a binary system of zero and one. We collect the elements of the Galois field of order 8 with the projective matrix. We have seven projective matrices, and we found the shortest distance between two different points of the matrices where the highest distance that we got is 585, and the shortest distance is 73. And we test the code. Hence the maximum value of code size on an eighth-order finite domain and an incidence matrix with parameters generated were, n (code length), d (minimum code), e (correction of error in the code). We test the code in coding theory as the code length is 581, the minimum code is 73 and error correction in the code is 36. We apply the coding theory to see if it is perfect or not perfect.

Keywords

• finite projective,,
• ,،؛space coding theory,,
• ,،؛incidence matrix linear code,,
• ,،؛perfect codes