Unformatted text preview: r j . [ Remark. The calculations required here are linear interpolations—ﬁnding the equation of the line through two given points ( α i ,r i ) and ( α j ,r j ).] ( b ) In ( a ), one polynomial f ( x ) should have come up as f i,j ( x ) much more often than any of the others. Give f = ev α,v ( f ( x )). We decode r to f = ev α,v ( f ( x )). ( c ) Give the minimum distance of the code C , and use that to justify the decoding guess of ( b ). 3. Problem 5.1.2 from the Notes . ( Hint: Consider canonical generator matrices for the two versions of the code. Remember that permuting the rows of a generator matrix for C gives a second generator matrix for C .)...
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- Spring '11
- Coding theory, Hamming Code, Linear code, linear polynomial fi,j, canonical generator matrices