A decoding algorithm for Twisted Gabidulin codes

In this work, we modify the decoding algorithm for subspace codes by Koetter and Kschischang to get a decoding algorithm for (generalized) twisted Gabidulin codes. The decoding algorithm we present applies to cases where the code is linear over the base field $\mathbb{F}_q$ but not linear over $\mathbb{F}_{q^n}$.Comment: This paper was submitted to ISIT 201

Coding Solutions for the Secure Biometric Storage Problem

The paper studies the problem of securely storing biometric passwords, such as fingerprints and irises. With the help of coding theory Juels and Wattenberg derived in 1999 a scheme where similar input strings will be accepted as the same biometric. In the same time nothing could be learned from the stored data. They called their scheme a "fuzzy commitment scheme". In this paper we will revisit the solution of Juels and Wattenberg and we will provide answers to two important questions: What type of error-correcting codes should be used and what happens if biometric templates are not uniformly distributed, i.e. the biometric data come with redundancy. Answering the first question will lead us to the search for low-rate large-minimum distance error-correcting codes which come with efficient decoding algorithms up to the designed distance. In order to answer the second question we relate the rate required with a quantity connected to the "entropy" of the string, trying to estimate a sort of "capacity", if we want to see a flavor of the converse of Shannon's noisy coding theorem. Finally we deal with side-problems arising in a practical implementation and we propose a possible solution to the main one that seems to have so far prevented real life applications of the fuzzy scheme, as far as we know.Comment: the final version appeared in Proceedings Information Theory Workshop (ITW) 2010, IEEE copyrigh

A Polynomial Description of the Rijndael Advanced Encryption Standard

The paper gives a polynomial description of the Rijndael Advanced Encryption Standard recently adopted by the National Institute of Standards and Technology. Special attention is given to the structure of the S-Box.Comment: 12 pages, LaTe

Unitary Space Time Constellation Analysis: An Upper Bound for the Diversity

The diversity product and the diversity sum are two very important parameters for a good-performing unitary space time constellation. A basic question is what the maximal diversity product (or sum) is. In this paper we are going to derive general upper bounds on the diversity sum and the diversity product for unitary constellations of any dimension $n$ and any size $m$ using packing techniques on the compact Lie group U(n).Comment: 15 pages, 3 figures, submitted to IEEE trans. inf

A Numerical Approach for Designing Unitary Space Time Codes with Large Diversity

A numerical approach to design unitary constellation for any dimension and any transmission rate under non-coherent Rayleigh flat fading channel.Comment: 32 pages, 6 figure

Some Remarks on Real and Complex Output Feedback

We provide some new necessary and sufficient conditions which guarantee arbitrary pole placement of a particular linear system over the complex numbers. We exhibit a non-trivial real linear system which is not controllable by real static output feedback and discuss a conjecture from algebraic geometry concerning the existence of real linear systems for which all static feedback laws are real

A Complete Characterization of Irreducible Cyclic Orbit Codes

We give a complete list of orbit codes that are generated by an irreducible cyclic group, i.e. an irreducible group having one generator. We derive some of the basic properties of these codes such as the cardinality and the minimum distance.Comment: in Proceedings of The Seventh International Workshop on Coding and Cryptography 2011 April 11-15 2011, Paris, Franc