1,040 research outputs found
Construction of Quasi-Cyclic Product Codes
Linear quasi-cyclic product codes over finite fields are investigated. Given
the generating set in the form of a reduced Gr{\"o}bner basis of a quasi-cyclic
component code and the generator polynomial of a second cyclic component code,
an explicit expression of the basis of the generating set of the quasi-cyclic
product code is given. Furthermore, the reduced Gr{\"o}bner basis of a
one-level quasi-cyclic product code is derived.Comment: 10th International ITG Conference on Systems, Communications and
Coding (SCC), Feb 2015, Hamburg, German
Self-Dual and Complementary Dual Abelian Codes over Galois Rings
Self-dual and complementary dual cyclic/abelian codes over finite fields form
important classes of linear codes that have been extensively studied due to
their rich algebraic structures and wide applications. In this paper, abelian
codes over Galois rings are studied in terms of the ideals in the group ring
, where is a finite abelian group and
is a Galois ring. Characterizations of self-dual abelian codes have been given
together with necessary and sufficient conditions for the existence of a
self-dual abelian code in . A general formula for the
number of such self-dual codes is established. In the case where
, the number of self-dual abelian codes in
is completely and explicitly determined. Applying known results on cyclic codes
of length over , an explicit formula for the number of
self-dual abelian codes in are given, where the Sylow
-subgroup of is cyclic. Subsequently, the characterization and
enumeration of complementary dual abelian codes in are
established. The analogous results for self-dual and complementary dual cyclic
codes over Galois rings are therefore obtained as corollaries.Comment: 22 page
Improved Lower Bounds for Constant GC-Content DNA Codes
The design of large libraries of oligonucleotides having constant GC-content
and satisfying Hamming distance constraints between oligonucleotides and their
Watson-Crick complements is important in reducing hybridization errors in DNA
computing, DNA microarray technologies, and molecular bar coding. Various
techniques have been studied for the construction of such oligonucleotide
libraries, ranging from algorithmic constructions via stochastic local search
to theoretical constructions via coding theory. We introduce a new stochastic
local search method which yields improvements up to more than one third of the
benchmark lower bounds of Gaborit and King (2005) for n-mer oligonucleotide
libraries when n <= 14. We also found several optimal libraries by computing
maximum cliques on certain graphs.Comment: 4 page
Self-dual cyclic codes over finite chain rings
Let be a finite commutative chain ring with unique maximal ideal , and let be a positive integer coprime with the
characteristic of . In this paper, the algebraic
structure of cyclic codes of length over is investigated. Some new
necessary and sufficient conditions for the existence of nontrivial self-dual
cyclic codes are provided. An enumeration formula for the self-dual cyclic
codes is also studied.Comment: 15 page
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