id: 02076753
dt: j
an: 02076753
au: Minbashian, F.David
ti: The group structure of irreducible polynomials over finite fields.
so: JP J. Algebra Number Theory Appl. 2, No. 3, 241-268 (2002).
py: 2002
pu: Pushpa Publishing House, Allahabad, Uttar Pradesh, India
la: EN
cc: 
ut: finite fields; coding theory; polynomials
ci: 
li: 
ab: The author identifies the finite field $\Bbb F_{q^n}$ of $q^n$ elements
    with the linear space $\Bbb F_q^n$ and studies the structure of
    (linear) codes $V_f$ consisting of the zeros in $\Bbb F_{q^n}$ of a
    (linearized) polynomial $f$ over $\Bbb F_q$. To each $f$, a finite
    Abelian group $G_f$ is constructed and algorithms for finding
    generators of $G_f$ and elements of the corresponding classes of
    polynomials consisting of irreducibles having the same order and rank
    are presented. A simple connection between cyclic codes and the $V_f$
    is established and examples of codes which beat the Gilbert-Varshamov
    bound are given.
rv: Arne Winterhof (Linz)