課程名稱︰ 編碼學(一)
課程教師︰ 黃漢水
開課系所︰ 數學系
考試時間︰ 2006/6/15
試題 :
一 The following ISBN have been received with smudges.
What are the missing digits. (20%)
0-6a8-50298-9, 1-12-433b525
二 Let C be a binary linear code having the following parity-check matrix
_ _
| 1 0 1 1 1 0 0 | (30%)
H = | 0 1 0 1 1 1 0 |
|_ 0 0 1 0 1 1 1 _|
(1) Find a parity-check matrix for C in standard form.
(2) Find a generator matrix for C in standard form.
(3) Find the minimum distance of C.
(4) Decode the received vectors 1010001, 0111101, 1001101.
(5) Is C a cyclic code ? Prove your answer.
三 Let C be a ternary linear code having the following generator matrix
_ _
G = | 2 1 1 0 | (30%)
|_1 1 0 2_|
(1) Find a generator matrix for C in standard form.
(2) Find a parity-check matrix for C in standard form.
(3) Find the minimum distance of C.
(4) Decode the received vectors 2112, 1021.
(5) Is C a cyclic code ? Prove your answer.
四 Let C be the binary Hamming code Ham(4, 2). (20%)
(1) Find the number of codewords of weight 3 in C.
(2) Find the number of codewords of weight 4 in C.
[ Hint : C is a perfect[15, 11, 3] code.]
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