Applications of Matroid Theory in Coding Theory II
Org:
Edgar Martínez Moro (University of Valladolid)
[
PDF]
 IRENE MÁRQUEZ CORBELLA, University of Valladolid (Spain)
Matroid decomposition and minimal codewords II [PDF]

The sets of minimal codewords in linear codes were considered for the first time in connection with decoding algorithms. It is well known that they are the set of minimal cycles of repesentable matroids. In this talk we will show how the Seymour's theory of decomposition helps in algebraically computing the generating set of the minimal codewords of the code.
 EDGAR MARTÍNEZ MORO, University of Valladolid (Spain)
Matroid decomposition and minimal codewords [PDF]

The sets of minimal codewords in linear codes were considered for the first time in connection with decoding algorithms. It is well known that they are the set of minimal cycles of repesentable matroids. In this talk we will show how the Seymour's theory of decomposition helps in algebraically computing the generating set of the minimal codewords of the code.
 PRADEEP SARVEPALLI, University of British Columbia
Quantum codes and symplectic matroids [PDF]

The correspondence between linear codes and representable matroids is well known. But a similar correspondence between quantum codes and matroids is not known. We show that representable symplectic matroids over a finite field $\mathbb{F}_q$ correspond to $\mathbb{F}_q$linear quantum codes. Although this connection is straightforward, it does not appear to have been made earlier in literature. Furthermore, we give an application of these results for quantum secret sharing schemes.
 KEISUKE SHIROMOTO, Kumamoto University (Japan)
Codes over rings and matroids. [PDF]

We consider a class of generalizations of matroids, called demimatroids, which have a duality property. This talk shall give some fundamental results on demimatroids including duality theorems, et al., and a construction of demimatroids from linear codes over finite quasiFrobenious rings. Then we apply some results on demimatroids to linear codes over these rings and show duality theorems such as a Weitype duality of generalized Hamming weights for these rings.
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