Concatenated structure and construction of certain code families

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Saçıkara Karıksız, Elif (2018) Concatenated structure and construction of certain code families. [Thesis]

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Abstract

In this thesis, we consider concatenated codes and their generalizations as the main tool for two different purposes. Our first aim is to extend the concatenated structure of quasi-cyclic codes to its two generalizations: generalized quasi-cyclic codes and quasi-abelian codes. Concatenated structure have consequences such as a general minimum distance bound. Hence, we obtain minimum distance bounds, which are analogous to Jensen's bound for quasi-cyclic codes, for generalized quasicyclic and quasi-abelian codes. We also prove that linear complementary dual quasi-abelian codes are asymptotically good, using the concatenated structure. Moreover, for generalized quasi-cyclic and quasi-abelian codes, we prove, as in the quasi-cyclic codes, that their concatenated decomposition and the Chinese Remainder decomposition are equivalent. The second purpose of the thesis is to construct a linear complementary pair of codes using concatenations. This class of codes have been of interest recently due to their applications in cryptography. This extends the recent result of Carlet et al. on the concatenated construction of linear complementary dual codes.
Item Type: Thesis
Uncontrolled Keywords: Concatenated codes. -- Generalized concatenated codes. -- Quasi-cyclic codes. -- Generalized quasi-cyclic codes. -- Quasi-abelian codes. -- Linear complementary dual codes. -- Linear complementary pair of codes. -- Birleştirmeli kodlar,. -- Genelleştirilmiş birleştirmeli kodlar. -- Sanki devirsel kodlar. -- Genelleştirilmiş sanki devirsel kodlar. -- Sanki değişmeli kodlar. -- Doğrusal bütünleyici kodlar. -- Doğrusal bütünleyici kod ikilileri.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 04 Oct 2018 09:20
Last Modified: 26 Apr 2022 10:26
URI: https://research.sabanciuniv.edu/id/eprint/36601

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