4 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
On the decoding of quasi-BCH codes
In this paper we investigate the structure of quasi-BCH codes. In the first part of this paper we show that quasi-BCH codes can be derived from Reed-Solomon codes over square matrices extending the known relation about classical BCH and Reed-Solomon codes. This allows us to adapt the Welch-Berlekamp algorithm to quasi-BCH codes. In the second part of this paper we show that quasi-BCH codes can be seen as subcodes of interleaved Reed-Solomon codes over finite fields. This provides another approach for decoding quasi-BCH codes