Find all the singularities of the function .
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Consider and the closed circular region
. Find points in R where |f(z)| has its maximum and minimum values.
Factor x5 - 1 over . Give the generator polynomials of all cyclic codes of length five over
.
Let and
be two binary codes with generator matrices
respectively.
i) Find the minimum distance of both the codes.
Table 1: Table for F16.
| 0000 | 0 | 1000 | α³ | 1011 | α⁷ | 1110 | α¹¹ |
|---|---|---|---|---|---|---|---|
| 0001 | 1 | 0011 | α⁴ | 0101 | α⁸ | 1111 | α¹² |
| 0010 | α | 0110 | α⁵ | 1010 | α⁹ | 1101 | α¹³ |
| 0100 | α² | 1100 | α⁶ | 0111 | α¹⁰ | 1001 | α¹⁴ |
Find the image of the semi-infinite strip x > 0, 0 < y < 1 when . Sketch the strip and its image.
) For the binary, (6,3) linear code C with generator matrix
prepare a standard array for decoding. Use it to decode the vectors (1, 1, 1, 0, 1, 1), and (1, 1, 0, 1, 1, 1). \hfill (7)
Find all the singularities of the function .
) Let C be the ternary [8,3] narrow-sense BCH code of designed distance , which has defining set
. Use the primitive root 8th root of unity you chose in 4a) to avoid recomputing the the table of powers. If
is the generator polynomial of C and
is the received word, find the transmitted codeword. Use the following table in 1.