課程名稱︰編碼學
課程性質︰數學系選修
課程教師︰黃漢水
開課系所︰數學系
考試時間︰九十二年六月
試題 :
1. The following ISBN have been received with smudges.
What are the missing digits.
(1) 0-13-2a72541
(2) 1-02-3443b25
2. Let C is a k-dimensional linear code in F(2,n).
Prove that either all the code-words have even weight
or exactly half have even weight and half have odd weight.
3. Let C be a binary linear code having teh following generator matrix
┌1 1 1 0 1 0 0┐
G = │0 1 1 1 0 1 0│
└0 0 1 1 1 0 1┘
(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 1110011 , 0011101 , 1011011
(5) Is C a cyclic code ? Prove your answer .
4. Let C be a ternary linear code having teh following parity-check matrix
H = ┌1 0 1 1┐
└2 2 0 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 1212 , 1221
(5) Is C a cyclic code ? Prove your answer .
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