On the factorization of trinomials over GF(3)

Pierre Loidreau

BP 105
78153 Le Chesnay Cedex, France

Fifth International Conference on Finite Fields and Applications,
Augsburg, Germany, 1999


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.