Lecture 7 : Explicit Linear Code Constructions
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چکیده
and α0, . . . , αn−1 are distinct elements in Fq. Typically, q = n and the αi’a are all thje elements of Fq, or n = q − 1 and the αi’s are all the nonzero elements of of Fq. The linearity of an RS code C can be easily verified by checking the conditions for closure under addition and scalar multiplication. Let c, c′ ∈ C be codewords corresponding to the messages m = (m0, . . . ,mk−1) and m′ = (m0, . . . ,m ′ k−1), respectively. Then c + c ′ is the encoding of the message (m0 +m0, . . . ,mk−1 +m ′ k−1) since
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