[SOLVED] CS MATH3411 INFORMATION, CODES & CIPHERS Test 1, Session 2 2011, SOLUTIONS

MATH3411 INFORMATION, CODES & CIPHERS Test 1, Session 2 2011, SOLUTIONS
Multiple choice: c,b,c,d,a True/False: T, F, F, T, T
(b): third block has 3 ones and the 20th bit is in that block. (c): The syndrome is 010.
(a): create a tree or 14 + 81 = (0.011)2.

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(b) False: Sphere packing bound implies |C| = 2k 2n
6. (a)True.w=d=7=23+1sothreecanbecorrected.
1+n+ 12n(n1) for 2-error correcting and n = 8, k = 3 does not satisfy this in-
(c) False: 1010 = c3+c3 = c4+c1. Alternatively, the Kraft-McMillan constant for this code is 98, so by the Kraft-McMillan theorem no UD code with the parameters of this code exists.
(d) True: K = 1 + 4 1 + 2 1 < 1. 3 9 27(e) True: Mp=pandsumofentriesofpis1.In order the codewords are 00, 10, 010, 110, 111, 0110, 0111. (b) Average length is 51.Multiple Choice: d, d, b, c, d True/False: F, T, T, F, T(d): last block has 3 ones and the 35th bit is in that block(b): Sphere packing bound implies |C| = 2 1 + n + 21n(n 1) for2-error correcting. The right-hand side of this inequality is 29 4.4,(c): Since that codeword has weight 7, w = d = 7 = 23+1 so threecan be corrected.(d): The Kraft-Macmillan constant is clearly greater than 1 in the firsttwocasesandforr=4weget31 +4 1 + 1 >1,butforr=5,
K=31+41+1 <1. 5 25125(a) False: second check equation is not satisfied. (b) True: multiply out the matrix and vector.(c) True: its an I-code (draw a tree).(d) False: c5 = 101 either by the tree or 41 +3 81 = 12 + 81 = (0.101)2.(e) True: Mp=pandsumofentriesofpis1.(a) In order the codewords are 01, 11, 000, 001, 101, 1000, 1001 (b) Average length is 52 = 13. CS: assignmentchef QQ: 1823890830 Email: [email protected]