{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

practicemidterm312

# practicemidterm312 - G denote a group having the just the 4...

This preview shows pages 1–2. Sign up to view the full content.

PRACTICE MIDTERM FOR MAT 312 (1) Let C Z 20 2 denote a set of code words. Suppose that d = 7 for this code. (a) How many transmission errors can be detected by this code? Explain why. (b) How many transmission errors can be corrected by this code? Ex- plain why. (c) Give a simple example of a code C with d = 7. (2) Let H denote a 4 × 6 binary matrix, and let C Z 6 2 denote all the binary 6-tuples c such that H c t = 0 . (a) Explain why C is a group code. In (b)-(e) below assume that H is equal to 0 0 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 Try do (b)-(d) without listing the code words in C . (b) Show that C is single error detecting and single error correcting. (c) Compute d for this code. (d) A code word c is transmitted and a binary 6-tuple r is received. If r = 110000 then compute the syndrome of r ; if at most one trans- mission error has been made, then find c . (e) List all the code words in C . (3)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: G denote a group having the just the 4 elements G = { a, b, c, d } . Suppose that ab = a and a 3 = c . (a) Which element of G is the identity. (b) ±ill in the multiplication table for G . (c) Is G isomorphic to Z 4 ? Is G isomorphic to Z 2 × Z 2 ? (4) Explain why each of the following pairs of groups are (or are not) iso-morphic. (a) Z 6 and Z 2 × Z 3 . (b) S 3 and Z 6 . (c) S 4 and S 3 . (d) S 2 and Z 2 . 1 2 PRACTICE MIDTERM FOR MAT 312 (5) Consider the permutation σ ∈ S 8 defned by σ = (126)(8241)(5368). (a) Write σ as a 2 × 8 matix having 1 2 3 4 5 6 7 8 For frst row. (b) Write σ-1 as a 2 × 8 matrix (as in part (a)). (c) Compute order ( σ ). (d) Write σ as a product oF disjoint cycles....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern