16 research outputs found
The dual of convolutional codes over
An important class of codes widely used in applications is the class of
convolutional codes. Most of the literature of convolutional codes is devoted
to con- volutional codes over finite fields. The extension of the concept of
convolutional codes from finite fields to finite rings have attracted much
attention in recent years due to fact that they are the most appropriate codes
for phase modulation. However convolutional codes over finite rings are more
involved and not fully understood. Many results and features that are
well-known for convolutional codes over finite fields have not been fully
investigated in the context of finite rings. In this paper we focus in one of
these unexplored areas, namely, we investigate the dual codes of convolutional
codes over finite rings. In particular we study the p-dimension of the dual
code of a convolutional code over a finite ring. This contribution can be
considered a generalization and an extension, to the rings case, of the work
done by Forney and McEliece on the dimension of the dual code of a
convolutional code over a finite field.Comment: submitte
Row reduced representations of behaviors over finite rings
Row reduced representations of behaviors over fields posses a number of useful properties. Perhaps the most important feature is the predictable degree property. This property allows a finite parametrization of the module generated by the rows of the row reduced matrix with prior computable bounds. In this paper we study row-reducedness of representations of behaviors over rings of the form , where is a prime number. Using a restricted calculus within we derive a meaningful and computable notion of row-reducedness
An iterative algorithm for parametrization of shortest length shift registers over finite rings
The construction of shortest feedback shift registers for a finite sequence
S_1,...,S_N is considered over the finite ring Z_{p^r}. A novel algorithm is
presented that yields a parametrization of all shortest feedback shift
registers for the sequence of numbers S_1,...,S_N, thus solving an open problem
in the literature. The algorithm iteratively processes each number, starting
with S_1, and constructs at each step a particular type of minimal Gr\"obner
basis. The construction involves a simple update rule at each step which leads
to computational efficiency. It is shown that the algorithm simultaneously
computes a similar parametrization for the reciprocal sequence S_N,...,S_1.Comment: Submitte