I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2011/2012, VOLUME 17, NUMBER 3, PAGES 5-23
Skew linear recurring sequences of maximal period over Galois rings
M. A. Goltvanitsa
S. N. Zaitsev
A. A. Nechaev
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a prime number,
be a Galois ring of
elements and of characteristic .
a Galois extension of the ring of
dimension and by the ring of
all linear transformations of the module .
We call a sequence over the
with the law of recursion
(i.e., a linear recurring sequence of order over the
module ) a skew LRS over .
It is known that the period of such
a sequence satisfies the inequality .
If , then we call
LRS of maximal period (a skew MP LRS) over .
A new general characterization of skew MP LRS in terms of
coordinate sequences corresponding to some basis of a free
module is given.
A simple constructive method of building a big enough class
of skew MP LRS is stated, and it is proved that the linear complexity
of some of them (the rank of the linear recurring sequence) over the
module is equal to
, i.e., to
the linear complexity over the module .
Last modified: May 4, 2012