Question: In each case, provide a GF that generates the sequence of coefficients: Consider the set of ternary numbers, T. An n-digit ternary number, tn =

In each case, provide a GF that generates the sequence of coefficients:

Consider the set of ternary numbers, T. An n-digit ternary number, tn = d1d2 . . . dn, has di ? {0, 1, 2}.

? How many n-digit ternary numbers are there?

? How many n-digit ternary numbers have an even digit sum, d1 + d2 + . . . + dn?

Consider the set of superternary numbers, S.

An n-digit superternary number, sn = ?1?2 . . . ?n, has ?i ? {1, 2, 3}.

? How many n-digit superternary numbers have an even digit sum, ?1 + ?2 + . . . + ?n? Consider the set of subternary numbers, R. An n-digit subternary number, rn = ?1?2 . . . ?n, has ?i ? {?1, 0, 1}.

? How many n-digit subternary numbers have an positive digit sum, ?1+?2+. . .+?n > 0?

In each case, provide a GF that generates the sequence of coefficients: Consider the set of ternary numbers, T. An n-digit ternary number, tn = did2 .. . dn, has di E {0, 1, 2}. . How many n-digit ternary numbers are there? . How many n-digit ternary numbers have an even digit sum, di + d2 + ... + dn? Consider the set of superternary numbers, S. An n-digit superternary number, Sn = 142 ... An, has Ai E {1, 2, 3}. . How many n-digit superternary numbers have an even digit sum, Al +2 + ... + An? Consider the set of subternary numbers, R. An n-digit subternary number, In = 6162 .. . on, has di E {-1, 0, 1}. . How many n-digit subternary numbers have an positive digit sum, 61+62+.. . ton > 0

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