North Maharashtra University 2008 B.Sc Mathematics S.YBSc MTH – 212 (B) (Computational Algebra) - university paper

18) Let e be the (3 , 8) encoding function with minimum distance 3. Let d
be the associated maximum likelihood decoding function. Determine
the number of errors that (e,d) can accurate.
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19) Let H =
? ? ? ?
?
?
? ? ? ?
?
?
0 1
1 0
0 1
1 1
be a parity check matrix. Decode 0101 relative to a
maximum likelihood decoding function associate with eH.
20) Let H =
? ? ? ?
?
?
? ? ? ?
?
?
0 1
1 0
0 1
1 1
be a parity check matrix. Decode 1101 relative to a
maximum likelihood decoding function associate with eH.
21) If H =
? ? ? ?
?
?
? ? ? ?
?
?
0 1
1 0
0 1
1 1
is a parity check matrix then obtain (2,4) group code
eH : B2 ? B4.
22) describe decoding function d : B9 ? B3 by d(y1y2y3y4y5y6y7y8y9) =
z1z2z3, where zi =
? ? ?
+ +
+ +
0, if (y , y , y ) has less than 2 1's
1, if (y , y , y ) has at lowest 2 1's
i i three i 6
i i three i six , one = i = 3.
Determine i) d(101111101) ii) d(100111100).
23) describe decoding function d : B9 ? B3 by d(y1y2y3y4y5y6y7y8y9) =
z1z2z3, where zi =
? ? ?
+ +
+ +
0, if (y , y , y ) has less than 2 1's
1, if (y , y , y ) has at lowest 2 1's
i i three i 6
i i three i six , one = i = 3.
Determine i) d(010000010) ii) d(011000011).
24) describe decoding function d : B6 ? B2 by d(y1y2y3y4y5y6) = z1z2,
where zi =
? ? ?
+ +
+ +
0, if (y , y , y ) has less than 2 1's
1, if (y , y , y ) has at lowest 2 1's
i i two i 4
i i two i four , one = i = 2.
Determine i) d(111011) ii) d(010100) iii) d(101011) ii) d(000110).
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2 : Multiple option ques. of one marks
1) If e : Bm ? Bn is an encoding function then - - - -
a) m < n and e is onto b) m < n and e is 1 one
c) m > n and e is onto d) m > n and e is 1 one
2) If x ? Bm then weight of x is - - - -
a) the number of 0’s in x b) the number of 1’s in x
c) the difference of the number of 1’s and the number of 0’s in x
d) m
3) If an encoding function e : Bm ? Bn is a parity check code then - -
- - - -
a) m = n + one b) n = m + one c) m = n d) n = m + m

Earning:   Approval pending.