Counting Irreducible Polynomials of Degree r over Fqn and Generating Goppa Codes Using the Lattice of Subfields of Fqnr. (17th September 2014)

• Record Type: Journal Article
• Authors: Magamba, Kondwani; Ryan, John A.
• Other Names: Gazeau Jean-Pierre Academic Editor.
• Is Part Of: Journal of discrete mathematics. Volume 2014(2014)
• Publication Date: 2014-09-17
• Subjects: Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.1155/2014/263179
• Languages: English
• ISSNs: 2090-9837

Abstract

Abstract : The problem of finding the number of irreducible monic polynomials of degreer overF q n is considered in this paper. By considering the fact that an irreducible polynomial of degreer overF q n has a root in a subfieldF q s ofF q n r if and only if( n r / s, r ) = 1, we show that Gauss's formula for the number of monic irreducible polynomials can be derived by merely considering the lattice of subfields ofF q n r . We also use the lattice of subfields ofF q n r to determine if it is possible to generate a Goppa code using an element lying in a proper subfield ofF q n r .