On additive cyclic codes

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Özdemir, Funda (2016) On additive cyclic codes. [Thesis]

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Abstract

In this thesis we consider two problems related to additive cyclic codes. In the first part, we obtain a lower bound on the minimum distance of additive cyclic codes via the number of rational points on certain algebraic curves over finite fields. This is an extension of the analogous bound for classical cyclic codes. Our result is the only general bound on such codes aside from Bierbrauer's BCH bound. We compare our bound's performance against the BCH bound for additive cyclic codes in a special case and provide examples where it yields better results. In the second part, we study complementary dual additive cyclic codes. We give a suficient condition for a special class of additive cyclic codes to be complementary dual.
Item Type: Thesis
Additional Information: Yükseköğretim Kurulu Tez Merkezi Tez No: 444537.
Uncontrolled Keywords: Additive cyclic code. -- Algebraic curve over a finite field. -- Hasse-Weil bound. -- BCH bound. -- Complementary dual code. -- Toplamsal devirsel kod. -- Sonlu bir cisim üzerinde cebirsel eğri. -- Hasse-Weil sınırı. -- BCH sınırı. -- Bütünleyici dual kod.
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: 16 Apr 2018 16:59
Last Modified: 26 Apr 2022 10:17
URI: https://research.sabanciuniv.edu/id/eprint/34463

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