課程名稱︰編碼學
課程性質︰數學系選修
課程教師︰黃漢水
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2009/06/18
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
一 The following ISBN have been received with smudges.
What are the missing digits.(10%)
0-658-5a237-1, 1-13-52424b5
二 Let C be a binary linear code having the following generator matrix
┌ ┐
│0 1 1 0 1 0 1│
G =│1 1 0 0 1 1 0│ (30%)
│1 1 1 1 0 0 0│
└ ┘
(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 1010001, 0111101, 1001101.
(5) Is C a cyclic code? Prove your answer.
三 Let C be a ternary linear code having the following parity-check matrix
┌ ┐
H =│1 2 0 1│ (30%)
│0 2 2 2│
└ ┘
(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 2202, 1122.
(5) Is C a cyclic code? Prove your answer.
四 Let F_3 = {0,1,2} and
T_k ={ f(x)屬於F_3[x] | f(x)is a monic irreducible polynomial of degree k }
(1) Find the set T_1, T_2. (7%)
(2) How many polynomials in the set T_3, T_4? Prove your answer. (8%)
五 Let C be a ternary [13,10,3] Linear code. (15%)
(1) How many codwords in C of weight 3? Prove your answer.
(2) How many codwords in C of weight 4? prove your answer.
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◆ From: 219.84.9.170
※ 編輯: sxq 來自: 219.84.9.170 (06/24 16:50)
※ 編輯: sxq 來自: 219.84.9.170 (06/24 16:50)