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Designs, Codes and Cryptography

, Volume 87, Issue 12, pp 3019–3043 | Cite as

Necessary field size and probability for MDP and complete MDP convolutional codes

  • Julia LiebEmail author
Article
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Abstract

It has been shown that maximum distance profile (MDP) convolutional codes have optimal recovery rate for windows of a certain length, when transmitting over an erasure channel. In addition, the subclass of complete MDP convolutional codes has the ability to reduce the waiting time during decoding. Since so far general constructions of these codes have only been provided over fields of very large size, there arises the question about the necessary field size such that these codes could exist. In this paper, we derive upper bounds on the necessary field size for the existence of MDP and complete MDP convolutional codes and show that these bounds improve the already existing ones. For some special choices of the code parameters, we are even able to give the exact minimum field size. Moreover, we derive lower bounds for the probability that a random code is MDP respective complete MDP.

Keywords

Convolutional codes Maximum distance profile Superregular matrices Finite fields 

Mathematics Subject Classification

94B10 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WuerzburgWuerzburgGermany

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