A Relation between Hadamard Codes and Some Special Codes over F2+uF2

Özkan, Mustafa; Öke, Figen

doi:10.18576/amis/100229

Cited by 5 publications

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“…Hadamard codes are called a code defined by Hadamard matrices. It says that using Hadamard matrices new codes could be obtained.This study is a generalizations of results obtained in [7,8,9] for the finite chain rings over 2  .…”

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confidence: 56%

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Extensions of Hadamard Codes Defined on Rings

Özkan

Öke

2018

ITM Web Conf.

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In this study, some special matrices are constructed by choosing certain elements from finite rings and certain codes are written by using these matrices.These codes are extended to a field. Moreover these codes are classified and more good codes are written. 4  ring were obtained by Krotov D. in [1] and [2]. Hadamard Code over 4  in particular were worked by Krotov D. in [2]. We will deal with codes defined over finite rings and binary codes. Main aim is to obtain new and good codes. An n . rank square matrix M that total ingredient 1 or 1  where t MM nI  is defined Hadamard matrix. Hadamard codes are called a code defined by Hadamard matrices. It says that using Hadamard matrices new codes could be obtained.This study is a generalizations of results obtained in [7,8,9] for the finite chain rings over 2  .

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mentioning

confidence: 56%

“…This study is a generalizations of results obtained in [7,8,9] for the finite chain rings over 2  .…”

mentioning

confidence: 56%

Extensions of Hadamard Codes Defined on Rings

Özkan

Öke

2018

ITM Web Conf.

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“…Hadamard codes were studied before in [5]. Especially, A relation between Hadamard codes and some special codes over F 2 + uF 2 was studied by M. Özkan and F. Öke in [1]. In this paper a relation between Hadamard codes and some special codes over the rings…”

Section: Introductionmentioning

confidence: 96%

Codes Defined via Especial Matrices over the Ring and Hadamard Codes

Özkan¹,

Öke²

2017

Mathematical Sciences and Applications E-Notes

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“…Özkan and F. Öke in [1]. This last study,which was written by forming special matrices over the ring is the Pioneer reference for emergance of this article.…”

Section: Introductionmentioning

confidence: 99%

Repeat Codes, Even Codes, Odd Codes and Their Equivalence

Özkan¹,

Öke²

2017

GLM

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Codes over the chain ring are obtained by writing special matrices. Gray images of these codes are binary codes. It is shown that first repeat code, second repeat code, even code and odd code are either equivalent or equal to these codes. The definitions of direct sum and direct product of these codes were given. Moreover dual codes were classed. Self dual codes and self orthogonal codes were established. Keywords : Codes over rings, Lee distance, Even codes, Odd codes, Dual codes. MSC No: 94B15, 94B60. IntroductionDifferent codes over the ring 22 u   with 2 0 u  were studied before. Generally the relation between the codes over 22 u   and binary codes were established. Some of these studies ;(1 ) u  cyclic and cyclic codes over the ring 22 u   were studied by J.F.Qian, L.N.Zhang and S.X Zhu in [3]. Some results on cyclic codes over 22 v   were studied by S. Zhu, Y. Wang and M. Shi in [9]. A relation between Hadamard codes and some special codes over 22 u   were studied by M.Özkan and F. Öke in [1]. This last study,which was written by forming special matrices over the ring is the Pioneer reference for emergance of this article. In this study, codes over the ring 22 u   are written by using special matrix. Special types of Hadamard codes ara discussed finding binary of these codes.In the second section, basic code structure was described as weigth function on the ring 22 u   and information about Hadamard codes were given. Gray map was defined. Matrices

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A Relation between Hadamard Codes and Some Special Codes over F2+uF2

Cited by 5 publications

References 0 publications

Extensions of Hadamard Codes Defined on Rings

Extensions of Hadamard Codes Defined on Rings

Codes Defined via Especial Matrices over the Ring and Hadamard Codes

Repeat Codes, Even Codes, Odd Codes and Their Equivalence

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