170 research outputs found
Maximal curves from subcovers of the GK-curve
For every with a prime power greater than , the GK-curve is an
-maximal curve that is not -covered by the
Hermitian curve. In this paper some Galois subcovers of the GK curve are
investigated. We describe explicit equations for some families of quotients of
the GK-curve. New values in the spectrum of genera of -maximal
curves are obtained. Finally, infinitely many further examples of maximal
curves that cannot be Galois covered by the Hermitian curve are provided
On the difference between permutation polynomials over finite fields
The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990,
states that if , then there is no complete mapping polynomial
in \Fp[x] of degree . For arbitrary finite fields \Fq, a
similar non-existence result is obtained recently by I\c s\i k, Topuzo\u glu
and Winterhof in terms of the Carlitz rank of .
Cohen, Mullen and Shiue generalized the Chowla-Zassenhaus-Cohen Theorem
significantly in 1995, by considering differences of permutation polynomials.
More precisely, they showed that if and are both permutation
polynomials of degree over \Fp, with , then the
degree of satisfies , unless is constant. In this
article, assuming and are permutation polynomials in \Fq[x], we
give lower bounds for in terms of the Carlitz rank of
and . Our results generalize the above mentioned result of I\c s\i k et
al. We also show for a special class of polynomials of Carlitz rank that if is a permutation of \Fq, with , then
Cyclotomic function fields over finite fields with irreducible quadratic modulus
Let be the finite field of order and
the rational function field. In this paper, we give a characterization of the
cyclotomic function fields with modulus , where is a monic and irreducible polynomial of degree two. We also
provide the full automorphism group of in odd characteristic,
extending results of \cite{MXY2016} where the automorphism group of
over was computed
Locally recoverable codes from automorphism groups of function fields of genus
A Locally Recoverable Code is a code such that the value of any single
coordinate of a codeword can be recovered from the values of a small subset of
other coordinates. When we have non overlapping subsets of cardinality
that can be used to recover the missing coordinate we say that a linear
code with length , dimension , minimum distance has
-locality and denote it by In this paper we provide a new upper bound for the minimum distance
of these codes. Working with a finite number of subgroups of cardinality
of the automorphism group of a function field of genus , we propose a construction of -codes and apply the results to some well known families
of function fields
Construction of sequences with high Nonlinear Complexity from the Hermitian Function Field
We provide a sequence with high nonlinear complexity from the Hermitian
function field over . This sequence was
obtained using a rational function with pole divisor in certain
collinear rational places on , where . In
particular we improve the lower bounds on the th-order nonlinear complexity
obtained by H. Niederreiter and C. Xing; and O. Geil, F. \"Ozbudak and D.
Ruano
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