some connection between algebraic structure and block codes some connection between algebraic...

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Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department of Computer Science, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran Co-authors: Arsham Borumand Saeid Hamideh Fatemidokht Cristina Flaut AAA90 The 90 th workshop on General Algebra 1

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Page 1: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

Some Connection between Algebraic Structure and Block

Codes

Marjan Kuchaki Rafsanjani

Department of Computer Science, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman,

Kerman, Iran

Co-authors:

Arsham Borumand SaeidHamideh Fatemidokht

Cristina Flaut

AAA90The 90th workshop on General Algebra 1

Page 2: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

Outline

IntroductionPreliminariesMain results Conclusion

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AAA90The 90th workshop on General Algebra

Page 3: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

Introduction

In this work, we studied the relationship between BCK-algebras, partially ordered sets and binary block codes.

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AAA90The 90th workshop on General Algebra

Page 4: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

Preliminaries

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Page 5: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

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Page 6: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

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Page 8: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

Main results

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Page 9: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

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Page 10: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

Constructing BCK-algebras from block codes

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Page 15: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

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Page 17: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

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Page 18: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

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Page 19: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

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Page 20: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

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Partial ordering.

Page 21: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

Conclusion

We showed that we can assign to any ordered structures a block codes and conversely.

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Page 22: Some Connection between Algebraic Structure and Block Codes Some Connection between Algebraic Structure and Block Codes Marjan Kuchaki Rafsanjani Department

Thank You…

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AAA90The 90th workshop on General Algebra