作者sxq (秋风泉)
看板NTU-Exam
标题[试题] 97下 黄汉水 编码学 期末考
时间Wed Jun 24 16:48:09 2009
课程名称︰编码学
课程性质︰数学系选修
课程教师︰黄汉水
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2009/06/18
考试时限（分钟）：120分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
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)属於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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※ 编辑: sxq 来自: 219.84.9.170 (06/24 16:50)
※ 编辑: sxq 来自: 219.84.9.170 (06/24 16:50)