TY - JOUR
T1 - Factorization of trinomials over galois fields of characteristic 2
AU - Vishne, Uzi
PY - 1997/10
Y1 - 1997/10
N2 - We study the parity of the number of irreducible factors of trinomials over Galois fields of characteristic 2. As a consequence, some sufficient conditions for a trinomial being reducible are obtained. For example,xn+axk+b∈GF(2t)[x] is reducible if bothn,tare even, except possibly whenn= 2k,kodd. The caset= 1 was treated by R. G. Swan (Pacific J. Math.12,No. 2 (1962), 1099-1106), who showed thatxn+xk+ 1 is reducible overGF(2) if 8|n.
AB - We study the parity of the number of irreducible factors of trinomials over Galois fields of characteristic 2. As a consequence, some sufficient conditions for a trinomial being reducible are obtained. For example,xn+axk+b∈GF(2t)[x] is reducible if bothn,tare even, except possibly whenn= 2k,kodd. The caset= 1 was treated by R. G. Swan (Pacific J. Math.12,No. 2 (1962), 1099-1106), who showed thatxn+xk+ 1 is reducible overGF(2) if 8|n.
UR - http://www.scopus.com/inward/record.url?scp=0031256843&partnerID=8YFLogxK
U2 - 10.1006/ffta.1997.0191
DO - 10.1006/ffta.1997.0191
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AN - SCOPUS:0031256843
SN - 1071-5797
VL - 3
SP - 370
EP - 377
JO - Finite Fields and Their Applications
JF - Finite Fields and Their Applications
IS - 4
ER -