2021•Iraqi Journal of ScienceOpen access

Certain Types of Linear Codes over the Finite Field of Order Twenty-Five

Emad Bakr Al-Zangana, Elaf Abdul Satar Shehab

Abstract

The aim of the paper is to compute projective maximum distance separable codes, -MDS of two and three dimensions with certain lengths and Hamming weight distribution from the arcs in the projective line and plane over the finite field of order twenty-five. Also, the linear codes generated by an incidence matrix of points and lines of were studied over different finite fields.

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Key concepts: Finite field, Projective plane, Mathematics, Finite geometry, Weight distribution, Hamming distance, Hamming code, Order (exchange)