On a hypothese concerning irreducible trinomials over GF(2)

Andrzej Paszkiewicz. "On a hypothese concerning irreducible trinomials over GF(2)." Mathematica Applicanda 37.51/10 (2009): null. <http://eudml.org/doc/292741>.

@article{AndrzejPaszkiewicz2009,
abstract = {In this paper all irreducible and lexicographically youngest polynomials overthe binary field GF(2) and degrees between 10000 to 20000 have been enumerated. Each of these polynomials has a specific structure: it can be expressed in the form n + g(X), where g(X) is a polynomial with very low degree in comparison to n and dependingon n. A hypothesis mentioned in the title addresses to the maximal growth rate thedegree of g(X) as a function of n. By the way we discuss other conjectures concerningrelations between the degree of g(X)and . All computations were performed by the aidof distributed computing technique in a small computer network consisting of few IBMPC work stations.},
author = {Andrzej Paszkiewicz},
journal = {Mathematica Applicanda},
keywords = {irreducible polynomials, finite fields.},
language = {eng},
number = {51/10},
pages = {null},
title = {On a hypothese concerning irreducible trinomials over GF(2)},
url = {http://eudml.org/doc/292741},
volume = {37},
year = {2009},
}

TY - JOUR
AU - Andrzej Paszkiewicz
TI - On a hypothese concerning irreducible trinomials over GF(2)
JO - Mathematica Applicanda
PY - 2009
VL - 37
IS - 51/10
SP - null
AB - In this paper all irreducible and lexicographically youngest polynomials overthe binary field GF(2) and degrees between 10000 to 20000 have been enumerated. Each of these polynomials has a specific structure: it can be expressed in the form n + g(X), where g(X) is a polynomial with very low degree in comparison to n and dependingon n. A hypothesis mentioned in the title addresses to the maximal growth rate thedegree of g(X) as a function of n. By the way we discuss other conjectures concerningrelations between the degree of g(X)and . All computations were performed by the aidof distributed computing technique in a small computer network consisting of few IBMPC work stations.
LA - eng
KW - irreducible polynomials, finite fields.
UR - http://eudml.org/doc/292741
ER -