Some Applications of Coding Theory in the Projective Plane of Order Four

Najm A. M. AL-Seraji, Hamza L. M. Ajaj

Abstract


The main aim of this research is to introduce the relationship between the topic of coding theory and the projective plane of order four. The maximum value of size code M over the finite field of order four and an incidence matrix with the parameters, n (length of code), d (minimum distance of code) and e (error-correcting of code) have been constructed. Some examples and theorems have been given.

Keywords


: projective plane, coding theory, incidence matrix.

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References


J.W.P. Hirschfeld, "Coding Theory" Lectures, Sussex University, UK, 2014.

R. Hill, "A first course in coding theory", Clarendon Press, Oxford, 1986.

N.A.M. Al-Seraji, "The Geometry of The Plane of order Seventeen and its Application to Error-correcting Codes", Ph.D. Thesis, University of Sussex, UK, 2010.

E. M. Al-Zangana, "The Geometry of The Plane of order Nineteen and its Application to Error-correcting Codes" Ph.D. Thesis, University of Sussex, UK, 2011.




DOI: http://dx.doi.org/10.23851/mjs.v30i1.544

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