Question a a consumer organization wishes to test 12

Assignment Help Mathematics

Reference no: EM13372335

Question

(a) A consumer organization wishes to test 12 different new perfumes, and has devised a number of tests to accomplish this. These tests are subject the following constraints:

• only six perfumes are to be tested by each tester;

• each pair of perfumes is to be compared the same number of times.

(i) Explain how a block design can be used to set up this experiment.

(ii) Find the set of parameters (v, b, k, r, λ) of such a design where the number of testers is as small as possible. List one other appropriate set of parameters for such a design.

(iii) Use a construction (from those described in Design 4) to construct such a design for which the number of testers is as small as possible.

(b) Let Δ be a BIBD with k = 5 and λ = 2. Explain why the number of varieties in Δ must have either the form 10n + 1 or the form 10n + 5, for some integer n.

(ii) Is a design as in part (b) with v = 21 resolvable?

Explain your answers briefly.

(d) Let Δ be a BIBD, let Δ^_ be its complement, and let C and C^_ be the codes whose codcwords are the rows of the incidence matrices of Δ and Δ^_, respectively.

Show that the codes C and C^- have the same Hamming distance.

Reference no: EM13372335

Questions Cloud

Part-1use one business rule delivery fees consist of a : part-1use one business rule delivery fees consist of a fixed amount of 1000 per truck plus carbon emission charge and

Introductionthe role of an information systems project : introductionthe role of an information systems project manager to produce a project initiation document pid for your

You will implement an end-to-end document classication : you will implement an end-to-end document classi?cation system that predicts which category pages belong to using the

1 industry demand function q 14 - frac12p 0001income : 1. industry demand function q 14 - frac12p 0.001income. marginal cost is fixed and equal to 16. fixed costs 0. you

Question a a consumer organization wishes to test 12 : question a a consumer organization wishes to test 12 different new perfumes and has devised a number of tests to

Question capital gains taxin july 2011 the labour party put : question capital gains taxin july 2011 the labour party put forward a proposal to have a comprehensive capital gains

Implementation of both the algorithms using cc code 1 : implementation of both the algorithms using cc code 1. roommates problem 2. intern problem1. the roommate problemthe

In this project you need to write a program called : in this project you need to write a program called ecc.javato implement elliptic curve

Project title email spam filterabstractanalyze the emails : project title email spam filterabstractanalyze the emails and predict whether the mail is a spam or not a spam.to work

User Account

All Pages