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The exact length of the Euclidean algorithm in F q [ X ]
Author(s) -
Knopfmacher Arnold,
Knopfmacher John
Publication year - 1988
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s002557930001528x
Subject(s) - mathematics , euclidean geometry , euclidean algorithm , combinatorics , range (aeronautics) , euclidean distance , finite field , field (mathematics) , discrete mathematics , pure mathematics , geometry , materials science , composite material
A study is made of the length L ( h, k ) of the Euclidean algorithm for determining the g.c.d. of two polynomials h , k inF q[ X ],F qa finite field. We obtain exact formulae for the number of pairs with a fixed length N which lie in a given range, as well as the average length and variance of the Euclidean algorithm for such pairs.