DeepAI AI Chat
Log In Sign Up

State spaces of convolutional codes, codings and encoders

by   Štěpán Holub, et al.
Charles University in Prague

In this paper we give a compact presentation of the theory of abstract spaces for convolutional codes and convolutional encoders, and show a connection between them that seems to be missing in the literature. We use it for a short proof of two facts: the size of a convolutional encoder of a polynomial matrix is at least its inner degree, and the minimal encoder has the size of the external degree if the matrix is reduced.


page 1

page 2

page 3

page 4


Smaller Keys for Code-Based Cryptography: McEliece Cryptosystems with Convolutional Encoders

In this paper we present a novel class of convolutional codes and invest...

Noncatastrophic convolutional codes over a finite ring

Noncatastrophic encoders are an important class of polynomial generator ...

Convolutional codes with a maximum distance profile based on skew polynomials

We construct a family of (n,k) convolutional codes with degree δin k,n-k...

Uniquely optimal codes of low complexity are symmetric

We formulate explicit predictions concerning the symmetry of optimal cod...

Power Hadamard matrices and Plotkin-optimal p-ary codes

A power Hadamard matrix H(x) is a square matrix of dimension n with entr...

Systematic Maximum Sum Rank Codes

In the last decade there has been a great interest in extending results ...

Interpreting Training Aspects of Deep-Learned Error-Correcting Codes

As new deep-learned error-correcting codes continue to be introduced, it...