67 research outputs found
A family of constacyclic codes over and its application to quantum codes
We introduce a Gray map from to
and study -constacyclic codes over
where It is proved that
the image of a -constacyclic code length over
under the Gray map is a
distance-invariant quasi-cyclic code of index and length over
We also prove that every code of length which is the
Gray image of cyclic codes over of
length is permutation equivalent to a binary quasi-cyclic code of index
Furthermore, a family of quantum error-correcting codes obtained from the
Calderbank-Shor-Steane (CSS) construction applied to -constacyclic codes
over $\mathbb{F}_{2^{m}}+u\mathbb{F}_{2^{m}}.
-constacyclic codes over
Let be a finite field and be an indeterminate. This
article studies -constacyclic codes over the ring
where . We illustrate the generator polynomials and investigate the
structural properties of these codes via decomposition theorem
-constacyclic codes over
Let where denotes the ring of
integers modulo and . In the present paper, we introduce a new Gray
map from to We study -constacyclic codes
over of odd lengths with the help of cyclic codes over . It is proved
that the Gray image of -constacyclic codes of length over are
cyclic codes of length over . Further, a number of linear
codes over as the images of -constacyclic codes over
are obtained
-self-orthogonal constacyclic codes of length over
In this paper, we study the -self-orthogonality of constacyclic codes
of length over the finite commutative chain ring , where and is a ring automorphism of . First, we obtain the structure of -dual
code of a -constacyclic code of length over . Then, the necessary and sufficient conditions for a
-constacyclic code to be -self-orthogonal are provided. In
particular, we determine the -self-dual constacyclic codes of length
over . Finally, we extend the
results to constacyclic codes of length
Constacyclic Codes over
In this paper, we study constacyclic codes over , where is an
odd prime and . The polynomial generators of all constacyclic codes over
are characterized and their dual codes are also determined.Comment: 12 page
All -constacyclic codes of length over
Let be a finite field with cardinality and
with . We aim to determine
all -constacyclic codes of length over , where
, and
. Let and
. The residue ring is a chain ring with the maximal ideal
in the case that is
irreducible in . If is reducible in
, we give the explicit expressions of the ideals of
. Besides, the number of
codewords and the dual code of every -constacyclic code are
provided.Comment: arXiv admin note: text overlap with arXiv:1512.01406 by other author
An explicit representation and enumeration for self-dual cyclic codes over of length
Let be a finite field of cardinality and a
positive integer. Using properties for Kronecker product of matrices and
calculation for linear equations over , an efficient method
for the construction of all distinct self-dual cyclic codes with length
over the finite chain ring is
provided. On that basis, an explicit representation for every self-dual cyclic
code of length over and an exact
formula to count the number of all these self-dual cyclic codes are given
Skew constacyclic codes over Fq+uFq+vFq
In this paper skew constacyclic codes over finite non-chain ring R =
F_q+uF_q+vF_q, where q= p^m, p is an odd prime and u^{2}=u, v^{2}=v, uv = vu =
0 are studied. We show that Gray image of a skew alpha-constacyclic cyclic code
of length n over R is a skew alpha-quasi-cyclic code of length over F_{q}
of index 3. It is also shown that skew alpha-constacyclic codes are either
equivalent to alpha-constacyclic codes or alpha-quasi-twisted codes over R.
Further, the structural properties of skew constacyclic over R are obtained by
decomposition method.Comment: 10 pages paper communicated to the Journal of Algebra and its
Application
Constacyclic codes over F_q + u F_q + v F_q + u v F_q
Let q be a prime power and F_q be a finite field. In this paper, we study
constacyclic codes over the ring F_q+ u F_q +v F_q+ u v F_q, where u^2=u, v^2=v
and uv=vu. We characterized the generator polynomials of constacyclic codes and
their duals using some decomposition of this ring. We also define a gray map
and characterize the Gray images of self-dual cyclic codes over
F_q+uF_q+vF_q+uvF_q
Cyclic DNA codes over F2+uF2+vF2+uvF2
In this work, we study the structure of cyclic DNA codes of arbitrary lengths
over the ring R=F2+uF2+vF2+uvF2 and establish relations to codes over R1=F2+uF2
by defining a Gray map between R and R1^2 where R1 is the ring with 4 elements.
Cyclic codes of arbitrary lengths over R satisfied the reverse constraint and
the reverse-complement constraint are studied in this paper. The GC content
constraint is considered in the last
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