Quasi-Cyclic Codes

  • Marco BaldiEmail author
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)


In this chapter, we recall the main definitions concerning quasi-cyclic codes, which will be used in the remainder of the book. We introduce the class of circulant matrices, and the special class of circulant permutation matrices, together with their isomorphism with polynomials over finite fields. We characterize the generator and parity-check matrices of quasi-cyclic codes, by defining their “blocks circulant” and “circulants block” forms, and show how they translate into an encoding circuit. We define a special class of quasi-cyclic codes having the parity-check matrix in the form of a single row of circulant blocks, which will be of interest in the following chapters. Finally, we describe how to achieve efficient encoding algorithms based on fast polynomial multiplication and vector-circulant matrix products.


Quasi-cyclic codes Circulant matrices Generator matrix Parity-check matrix Polynomial representation Fast vector-by-circulant-matrix product 


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© The Author(s) 2014

Authors and Affiliations

  1. 1.DIIUniversitá Politecnica delle MarcheAnconaItaly

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