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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Irreducible congruences over $\textrm {GF}(2)$


Author: C. B. Hanneken
Journal: Trans. Amer. Math. Soc. 193 (1974), 291-301
MSC: Primary 12C05
DOI: https://doi.org/10.1090/S0002-9947-1974-0347782-4
MathSciNet review: 0347782
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Abstract: In characterizing and determining the number of conjugate sets of irreducible congruences of degree m belonging to $GF(p)$ relative to the group $G(p)$ of linear fractional transformations with coefficients belonging to the same field, the case $p = 2$ has been consistently excluded from considerations. In this paper we consider the special case $p = 2$ and determine the number of conjugate sets of m-ic congruences belonging to $GF(2)$ relative to $G(2)$.


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Keywords: Congruences, conjugate sets, transform of an <I>m</I>-ic congruence, conjugate under <I>G</I>, self-conjugate, mark of <IMG WIDTH="72" HEIGHT="45" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$GF({p^k})$">, irreducible and reducible congruences
Article copyright: © Copyright 1974 American Mathematical Society