33 research outputs found
Construction of Quasi-Cyclic Product Codes
Linear quasi-cyclic product codes over finite fields are investigated. Given
the generating set in the form of a reduced Gr{\"o}bner basis of a quasi-cyclic
component code and the generator polynomial of a second cyclic component code,
an explicit expression of the basis of the generating set of the quasi-cyclic
product code is given. Furthermore, the reduced Gr{\"o}bner basis of a
one-level quasi-cyclic product code is derived.Comment: 10th International ITG Conference on Systems, Communications and
Coding (SCC), Feb 2015, Hamburg, German
New Linear Codes from Matrix-Product Codes with Polynomial Units
A new construction of codes from old ones is considered, it is an extension
of the matrix-product construction. Several linear codes that improve the
parameters of the known ones are presented
One-Generator Quasi-Abelian Codes Revisited
The class of 1-generator quasi-abelian codes over finite fields is revisited.
Alternative and explicit characterization and enumeration of such codes are
given. An algorithm to find all 1-generator quasi-abelian codes is provided.
Two 1-generator quasi-abelian codes whose minimum distances are improved from
Grassl's online table are presented
New Linear Codes from Matrix-Product Codes with Polynomial Units
A new construction of codes from old ones is considered, it is an extension
of the matrix-product construction. Several linear codes that improve the
parameters of the known ones are presented
New algorithms for decoding in the rank metric and an attack on the LRPC cryptosystem
We consider the decoding problem or the problem of finding low weight
codewords for rank metric codes. We show how additional information about the
codeword we want to find under the form of certain linear combinations of the
entries of the codeword leads to algorithms with a better complexity. This is
then used together with a folding technique for attacking a McEliece scheme
based on LRPC codes. It leads to a feasible attack on one of the parameters
suggested in \cite{GMRZ13}.Comment: A shortened version of this paper will be published in the
proceedings of the IEEE International Symposium on Information Theory 2015
(ISIT 2015