'Primitive element' diaporamas de présentation

15-853:Algorithms in the Real World

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Reed-Muller and Preparata Codes

Reed-Muller and Preparata Codes. OUTLINE. [1] Reed-Muller codes [2] Decoding Reed-Muller codes [3] Extended Preparata Codes [4] Encoding Extended Preparata Codes [5] Decoding Extended Preparata Codes. Chap 3 Perfect and Related Codes. Recall [3.8]. Reed-Muller codes

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Cyclic Codes

Cyclic Codes. Hamming code is useful but there exist codes that offers same (if not larger) error control capabilities while can be implemented much simpler. Cyclic code is a linear code that any cyclic shift of a codeword is still a codeword.

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Introduction to Modern Cryptography Lecture 6

Introduction to Modern Cryptography Lecture 6 1. Testing Primitive elements in Z p 2. Primality Testing. 3. Integer Multiplication & Factoring as a One Way Function. Testing Primitive Elements mod p.

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296.3:Algorithms in the Real World

296.3:Algorithms in the Real World. Finite Fields review. Finite Fields Outline. Groups Definitions, Examples, Properties Multiplicative group modulo n Fields Definition, Examples Polynomials Galois Fields Why review finite fields?. Groups.

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Error control coding for wireless communication technologies

Error control coding for wireless communication technologies. Background material for Reed- Solomon and cyclic codes. EU-USA Atlantis Programme. FIT & Budapest University of Technology and Economics. Algebra over GF( p m ) .

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LDPC Codes Based on Cyclotomic Cosets Mina Sartipi and Faramarz Fekri Georgia Institute of Technology School of Electric

LDPC Codes Based on Cyclotomic Cosets Mina Sartipi and Faramarz Fekri Georgia Institute of Technology School of Electrical & Computer Engineering October 2003. Outline. Review of LDPC code Construction of cyclic LDPC codes using cyclotomic cosets

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236601 - Coding and Algorithms for Memories Lecture 13

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Basic Extensions for Computer Algebra System Domains

Basic Extensions for Computer Algebra System Domains. Lecture 2c. Preview: Extensions. if x is an indeterminate, and if D is a domain, we can talk about D[x], polynomials in x with coefficients in D or D(x) ratios of polys in x. Or D[[x]] : (truncated) power series in x over D.

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LOTF Chapter Two Notes

Fire on the Mountain. LOTF Chapter Two Notes. An atmosphere of freedom and merriment continues.

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Definitions

Definitions. group , ring and field polynomial over a field F degree of a polynomial over F F[x] degree of a polynomial in F[x] gcd of two polynomials from F[x] irreducible polynomial over F function induced by a polynomial root of a polynomial

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