Classification of the Projective Line Over Galois Field of Order Sixteen | ||
| Al-Mustansiriyah Journal of Science | ||
| Article 1, Volume 25, Issue 1, March 2014, Pages 119-128 | ||
| Author | ||
| N.A.M. Al-Seraji | ||
| Abstract | ||
| The main purpose of this paper is to classify certain geometric structure, called k-set, in a particular setting, namely the projective line of order sixteen PG(1,q^h), q=2,h=4. The subsets of the line PG(1,16), such the tetrads, the pentads, the hexads, the heptads and the octads are classified. The basic tool is the fundamental theorem of projective geometry; there is a unique projectivity of the projective line transforming three points to any three other points. Each of these k-sets gives rise to an error-correcting code that corrects the maximum possible number of errors for its lengths. | ||
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