” Math 3205程序 辅导 data程序 写作Math 3205 Assignment 5 December 2019Clearly write your answers to the questions showing all reasons, working and checks and indicate whateach mathematical calculation is doing. Do not erase anything. Include all rough work and do not commitplagiarism. Feel free to write explanations of what you are thinking at each stage, nothing you can writecan lose you marks!1. Let the addition table in Z2[] where 3 = + 1 be as follows:(a) Count how many latin squares there are within L of each cardinality (and explain why none existfor some cardinalities) from addition of subsets of the elements {0, 1, , + 1, 2, 2 + 1, 2 +, 2 + + 1}, keeping them in this order. [no need to count all permutations of them] [4]Francis Illya Xucheng Mingxin Aidan + 1 2 2 + 1 2 + (b) Using your randomly chosen element find the 88 latin square M which is formed using s+tfor the (s, t) entry using the elements. Do not just fill out the matrix, explain your process as yougo along. [4](c) Verify that M is orthogonal to L by highlighting all elements in L which are in the same placeas each of the elements of M in a different colour/shape/pattern and verify that the expectedbehaviour happens which proves orthogonality. [2]2. (a) Choose a prime number q congruent to 3(mod 4) (different from anyone else in the class you havetalked to) and find the squares mod q, use them to form the Paley design Pq for q, and verify thatany number appears in the same number of blocks with all other numbers. [2](b) Find the parameters v, b and r for Pq, give the incidence matrix and verify that k and satisfythe equations relating the parameters. [3](c) Create the Hadamard Matrix H corresponding to Pq and verify that HT H is a multiple of theidentity matrix, and list the 3-design based on it, verifying how many times a triple occurs. [3](d) Choose a block c of Pq and form either the derived or residual design with respect to c andcalculate the parameters. [2]如有需要，请加QQ：99515681 或邮箱：99515681@qq.com
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