Pierre Loidreau
INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France Pierre.Loidreau@inria.fr
Fifth International Conference on Finite Fields and
Applications,
Augsburg, Germany, 1999
Abstract
Trinomials play an important role in coding theory - they are in
particular the words of weight 3 of cyclic codes - and shift-register
sequences - being very easy to implement. Many things have been
written about trinomials over fields of characteristic 2, the parity
of their factorization, their order. Some of these results may be
extended to trinomials with coefficients in fields of odd
characteristic in a sometimes simpler way than for those with
coefficients in fields of even characteristic. The study of trinomials
over fields of odd characteristic has interesting properties
especially when they are taken over the finite field GF(3). In
particular wee show some parameters for which their are no possible
irreducible trinomials and for which their are no possible primitive
polynomials.