The Concatenated Structure of Quasi-Cyclic Codes and an Improvement of Jensen's Bound

Date

2013-02-01

Author

Guneri, Cem
Özbudak, Ferruh

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Following Jensen's work from 1985, a quasi-cyclic code can be written as a direct sum of concatenated codes, where the inner codes are minimal cyclic codes and the outer codes are linear codes. We observe that the outer codes are nothing but the constituents of the quasi-cyclic code in the sense of Ling-Sole. This concatenated structure enables us to recover some earlier results on quasi-cyclic codes in a simple way, including one of our recent results which says that a quasi-cyclic code with cyclic constituent codes are 2-D cyclic codes. In fact, we obtain a generalization of this result to multidimensional cyclic codes. The concatenated structure also yields a lower bound on the minimum distance of quasi-cyclic codes, as noted by Jensen, which we call Jensen's bound. We show that a recent lower bound on the minimum distance of quasi-cyclic codes that we obtained is in general better than Jensen's lower bound.

Subject Keywords

Concatenation, Constituents, Jensen's Bound, Multidimensional Cyclic Code, Quasi-Cyclic (QC) Code

URI

https://hdl.handle.net/11511/36691

Collections

Department of Mathematics, Article