Document Details
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Document Type |
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Thesis |
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Document Title |
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A comparative study of different weights on a class of rings: The homogenous weight vs The Lee weight دراسة مقارنة بين أوزان مختلفة على نوع من الحلقات: الوزن المتجانس و الوزن لي |
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Subject |
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Faculty of Sciences |
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Document Language |
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Arabic |
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Abstract |
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A great deal of interest has been given to codes over finite rings in the last two decades.Particularly,the family of Frobenius rings,which proved to be the largest family of rings to study for coding theory,according to J.Wood in 1999 CE,have generated a lot of research.Moreover,MacWilliams identities hold for codes over these rings.Many different Frobenius rings were studied within that context for reasons and motivations,leading to many results.Among the rings we study most often,we can name Galois rings, finite chain rings,etc. Various weight functions have also been of quite some interest in coding theory.The classical weight,that is the Hamming weight,is the usual weight most times,especially for codes over finite fields,as that leads to important results concerning the error cor rection capability of the code.Other weights have been for other applications. Among these weights are the Rosenbloom metric,the Lee metric and the homogeneous weight. Homogeneous weights were first introduced by I.Constantinescu and W.Heise in 1997 CE and later were considered within the confines of Frobenius rings by M.Greferath and S.E. Schmidt in 2000 CE.Various authors have defined, Lee weights for these rings together with suitable distance preserving Gray maps that map the codes to the corresponding binary codes. In this thesis,we will provide background for codes over a family of rings that we denote by Sq,m,together with a Lee weight over this ring with its associated Gray map. Using theoretical results about the homogeneous weight and the generating character we find a unique form for the homogeneous weight on Sq,m.Then,by assigning a specific value to the average weight,we find an associated Gray map for the homogeneous weight.Since both the Lee-Gray map and the homogeneous-Gray map map codes over Sq,m to codes over Fq, we compare the two weights by looking at the minimum distances of the |
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Supervisor |
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Dr. Adel Naif Al-Ahmadi |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1438 AH
2017 AD |
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Co-Supervisor |
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Dr. Najat Mohammad Muthana |
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Added Date |
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Sunday, May 28, 2017 |
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Researchers
| رحمه عطيه العمري | Alomari, Rahmah Atiah | Researcher | Master | |
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