coding2

coding2 - Subgroups 5 Fields Basic properties of fields 6...

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1 Coding for Communications Lecture 2 Finite Groups and Fields Galois fields and finite fields algebra
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2 Sets and operations over sets Groups Theorem: identity is unique Theorem: inverse is unique
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3 Example: modulo-2 addition Theorem: identity is unique Theorem: inverse is unique Example: modulo-m addition
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4 Example: modulo-p multiplication p-1 under (here order is intended in the sense of cardinality)
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Unformatted text preview: Subgroups 5 Fields Basic properties of fields 6 The binary field GF(2) Addition table in G={0,1,,6} 7 Multiplication table in G={0,1,,6} Is GF(7) a field? Yes How to do subtraction and division (ex: GF(7)) 8 With small integers we have the usual math rules With large integers we have overflow behaviour...
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coding2 - Subgroups 5 Fields Basic properties of fields 6...

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