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On Error Correcting Codes and Their Applications

Thesis Info

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Author

Asma Shaheen Ansari

Supervisor

Tariq Shah

Program

PhD

Institute

Quaid-I-Azam University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2017

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/10326

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726795170

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To expand the use of codes and provide a form of error-correction, it is useful to extend the use of binary streams into another representation. In this work, we have used different monoid rings for the construction of a new family of error correcting codes having better error correction capability. Initially we have constructed binary cyclic codes using monoid rings instead of polynomial ring. For an n length binary cyclic code, three di¤erent binary cyclic codes of length an; bn and abn are obtain. These codes are interleaved codes capable of correcting burst of errors alongwith random error correction. The BCH codes form a class of parameterized error-correcting codes which have been the subject of interest. Instead of primitive BCH codes we have showed the existence of non- primitive BCH codes of length bn over theelds F2, F4 andnite rings Z2m along with their applications. The value of b is investigated for which the existence of the non-primitive BCH code Cbn is assured. It is noticed that the code Cn is embedded in the code Cbn. Therefore, the data transmitted by the code Cn can also be transmitted by the code Cbn. The BCH codes Cbn have better error correction capability whereas the BCH code Cn has better code rate.
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