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Generalized quasi-cyclic codes: structural properties and code construction

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Abstract

Generalized quasi-cyclic (GQC) codes are defined by generator matrices comprised of circulant matrices of lengths not necessarily identical. A decomposition of these codes is given by using the Chinese reminder theorem. The focus is to characterize ρ-generator GQC codes in details. A good lower bound on the minimum distance of such a code in terms of the minimum distance of the constituent codes is given. Construction methods are given and a set of GQC codes is provided that from minimum distance perspective are optimal codes among the known linear codes having the same length and dimension.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran

    M. Esmaeili & S. Yari

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  1. M. Esmaeili
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  2. S. Yari
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Correspondence to M. Esmaeili.

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Esmaeili, M., Yari, S. Generalized quasi-cyclic codes: structural properties and code construction. AAECC 20, 159–173 (2009). https://doi.org/10.1007/s00200-009-0095-3

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  • DOI: https://doi.org/10.1007/s00200-009-0095-3

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