Bazı sonlu cisimler üzerinde esnek polinom kodlar

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JURİ

Bşkan

Doç. Dr. Hacı AKTAŞ danışmanlığ4nda _Şerİf

Öztü

taıafiıdan hazırlanan ''Bazı Sonlu Cisimler Üzerİnde

Esıek

Polinom

Kodlır''

başlıklı bu _ça1ışm4jürimiz tarafindan Nevşehiı Hacı Bektaş Veli Üniversitesi Fen Bilimleri Enstitiisü Matematik Anabilim

Dalında Doktorı Tezi olarak kabul edilmiştir.

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TEz BİIDİRİM

SAIT'ASI

Tez yazırıkıırallaıma uygun olarak hazırtanaİı _{bu çaıışınada}yer alan brtİın bilgilerin bilimsel ve akademik kurallaı _{çerçevesinde} elde edilerek sunulduğunu ve bana ait olınayan her t{İrlü ifade ve bilgiıin ka}'nağına ğksiksiz atıf yapıldığmı biıdiririr.

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vi

SOFT POLYNOMIAL CODES OVER SOME FINITE FIELDS (Ph. D. Thesis)

Şerif ÖZLÜ

NEVŞEHİR HACI BEKTAŞ VELİ UNIVERSITY

GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES April 2015

ABSTRACT

The purpose of this thesis, is to construct cyclic soft groups by using soft sets and to define cyclic soft codes by using these groups.

In the first section, history and progressing steps of coding theory and soft sets has been presented. In addition requriment of these concepts has been stated.

In the second section, a widely literature searching has been made about coding theory and basic properties of coding theory has been defined.

In the third section, a widely literature searching has been made and theoretical and practical studies has been mentioned about soft sets.

In the fourth section, orders of soft sets, cyclic soft groups and algebra properties of these groups has been studied. Also in this section cyclic soft codes has been constructed and anew generator matrix has been consisted of by using definition of cyclic soft codes. Hamming codes have been with these generator matrices.

In the fifth section, a new encoding method has been mentioned by using soft sets. This method creats soft encoding and error correcting algortithm.

Keywords: Soft sets, orders of Soft groups, soft cyclic groups, coding theory, soft cyclic codes, soft coding, soft decoding.

Thesis Supervisor: Assoc. Prof. Dr. Hacı AKTAŞ Page Number: 70

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