3 research outputs found
Convolutional Codes Derived From Group Character Codes
New families of unit memory as well as multi-memory convolutional codes are
constructed algebraically in this paper. These convolutional codes are derived
from the class of group character codes. The proposed codes have basic
generator matrices, consequently, they are non catastrophic. Additionally, the
new code parameters are better than the ones available in the literature.Comment: Accepted for publication in Discrete Mat
On cyclotomic cosets and code constructions
New properties of -ary cyclotomic cosets modulo , where is a prime power, are investigated in this paper. Based on these
properties, the dimension as well as bounds for the designed distance of some
families of classical cyclic codes can be computed. As an application, new
families of nonbinary Calderbank-Shor-Steane (CSS) quantum codes as well as new
families of convolutional codes are constructed in this work. These new CSS
codes have parameters better than the ones available in the literature. The
convolutional codes constructed here have free distance greater than the ones
available in the literature.Comment: Accepted for publication in Linear Algebra and its Application
Construction of Unit-Memory MDS Convolutional Codes
Maximum-distance separable (MDS) convolutional codes form an optimal family
of convolutional codes, the study of which is of great importance. There are
very few general algebraic constructions of MDS convolutional codes. In this
paper, we construct a large family of unit-memory MDS convolutional codes over
\F with flexible parameters. Compared with previous works, the field size
required to define these codes is much smaller. The construction also leads to
many new strongly-MDS convolutional codes, an important subclass of MDS
convolutional codes proposed and studied in \cite{GL2}. Many examples are
presented at the end of the paper