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
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)