(a) (i) Write down a parity-check matrix for the code Ham(2, 7). (ii) Using your parity-check matrix, explain why the minimum distance of Ham(2, 7) is exactly 3. (b) Consider the linear code C over F, with the following parity-check matrix: (3 1 1 0 2 30 1 (i) Decide whether or not C is an MDS code. Justify your answer. (ii) Suppose that the above matrix is instead taken to be the generator matrix of a linear code D over F7. Is D an MDS code? Justify your answer.

Q: compute in polynomial is P(x) =x° +x* +x²+x + 1. Given A(x) = x+x*+x°+x, find A'(x) mod P(x)

A: Given  The answer is given below.

Q: Es) Using truth tables, show that pay and (p → r) ^ (q → r) are not logically equivalem

A: Truth table of (p ∧ q)->r: p q r p ∧ q (p ∧ q)->r F F F F T F F T F T F T F F T F T…

Q: the LU factorization of the symmetric part of A(100*100)and verify that your factorization is…

A: In linear algebra, LU factorization, also called LU decomposition, is a technique that breaks down a…

Q: Using the Definitional proof, show that each of these functions is O(2²). (a) f(x)= 5x (b) f(x)= 5x…

A:

Q: Give the weight polynomial for the hamming code Ham3 (2), his parity-check-code Ĉ and for all in a…

A: #include <stdio.h> #include <math.h> int input[32]; int code[32]; int ham_calc(int,int);…

Q: Compute the result of applying a Hadamard transform to both qubits of |0> ⊗ |1> in two ways (the…

A: answer from step 2

Q: 4. The data-set X given below contains results of a vaccine trial. The data set contains a measure…

A: Answer: I have given answered in the handwritten format in brief explanation.

Q: 1) Determine the following properties(linearity ,time invariance,invertibility) for the system…

A: To determine the properties of linearity, time-in variance, and invertibility for the given system,…

Q: I'm having a bit of trouble understanding on question 2 how R is not symmetric, as each pair has its…

A: Induced relations on subsets can exhibit different properties than the original relation, as we saw…

Q: Question: Consider the (6, 3) linear code generated by the following matrix: [1 [G] = 0 Lo 0 0 0 1…

A: A digital system or technique that converts input data into a particular output representation in…

Q: 1) What is the VC dimension of a union of k intervals? In other words, you have k intervals and each…

A: Explanation:  The VC dimension of a union of k intervals is at most k.   The VC dimension of a set…

Q: Problem 5. Below you can see 8 matrices that describe symmetry operators: 100 -100 -100 100 -100 100…

A: As you have posted multiple questions, we will solve the first question for you.  1) The matrix…

Q: Let f : B 3 → B where f(x, y, z) = (x + z)y. (a) Provide a truth table for the function. (b) Derive…

A: In Boolean algebra, the canonical disjunctive normal form (DNF) and canonical conjunctive normal…

Q: 4- Determine the minimum expression for each K-map in figure below CD CD CD CD AB 1 1 1 AB 1 01 AB…

A: Determine the minimum expression for the K-map in the figure.

Q: Prove the De Morgan's Law - (p V q) =-pA-qusing the truth tables| p Vq -(p V q) 1 1

A: Here in this question we have asked to prove de morgan law using truth table.

Q: Convert the following CFG into Chomsky and Greibach Normal Forms: G=(N,T, P, E) N = {A, B} T = {x,…

A: Context-Free Grammars (CFGs) are used to describe the syntax of formal languages in computer science…

Q: 3. Given F(A,B,C,D,E) = TM (0,3,6,9,11,19,20,24,25,26,27,28,20,30). TTD (1,2,12,13). Find two…

A: 3.

Q: We can analyse cyclic codes using the fact that they correspond to certain subsets of the ring…

A: Answer: I have given answered in the handwritten format in brief explanation

Q: The linear combination of gcd(17, 23) is A (-4) x 17 + (4) x 23 B (3) x 17 + (-4) x 23 (-3) x 17 +…

A: Given GCD(17,23)

Q: 2. Given the following Maxterm Expansion. Plot the terms on a suitable K-Map and then (a) find out…

A: Given the following maxterm. We have to draw K-map for this and find Essential prime implicants and…

Q: Alice has asked you to help her classify these functions based on their asymptotic growth rate. That…

A:

Q: 3. Find the minimum sum-of-products expression for (a) Em(0, 2, 3, 5, 6, 7, 11, 12, 13) (b) Σ m(2,…

A: (a) Consider Σm(0, 2, 3, 5, 6, 7, 11, 12, 13) Prepare a Karnaugh map to find the minimum expression…

Q: If C is a linear code, with generator matrix G and parity-check matrix H , find a generator matrix G…

A: Solution :

Q: Show that (p →q)^(p → r) and t using method of Proof

A: Solution - In the given question, we have to show that the two given propositions are logically…

Q: olve C and D

A: Solution- The solution of above question is given as-

Q: Find the inverse of the matrix, Choices: 4 -3/2 1 3 3 4 1/2 c. 10 [7/2 3/2 -8 -4 -7/2 3/2 1/2l 1/2]…

A: Let A is a matrix, then inverse of matrix is: A-1=adj(A) ÷ |A| where adj(A) is a adjoint of matrix…

Q: Describe in words the language of the following CFG, then give a CFG for its complement which you…

A: Solution:  In Formal Language, a CFL is a language generated by some CFG.The set of all CFL is…

Q: show the sub problems based on the matrix chain multiplication for A x B x C x D

A: Solution: Here is the sub problems based on the matrix chain multiplication for ( A x B x C x D ).

Q: Use truth table to prove the equivalence of following (pvq) → r= (pr) ^ (q→r)

A: A truth table is a representation of mathematical table in which all possible outcomes would occur…

Q: Use the Basic Definition to prove that f (n) = 5n4 − 2n3 + n3 − 8n2 − 5n + 3 ∈ Ω(n4). For finding…

A: As you have posted multiple methods, we will solve the first method for you. In Ad-hoc method, to…

Q: a) Given a DFA M = (Q, Σ, δ, q0, F), consider M' = (Q, Σ, δ, q0, F'), where F' = Q − F. Prove that…

A: Automata, also known as finitе statе machinеs (FSMs), arе abstract modеls of computation that can bе…

Q: 2. Use Armstrong's axioms to prove the union rule: Ifαβ and α Y, then α-βy.

A: 2. The union rule to be proved using Armstrong's axioms are :  If α → β and α → γ, then α → βγ. The…

Q: Problem 1 (14 points)Show that the autocovariance function can be written asγ(s, t) = E[(xs − μs)(xt…

A: The objective of the question is to prove that the autocovariance function can be written in the…

Q: Obtain the root locus plot of   G(S)H(S) = k(S+3)(S+4)/(S+5)(S+6);  Determine the poles for gain k…

A: MATLAB CODE: clear all s = tf('s'); GH = ((s+3)*(s+4))/((s+5)*(s+6)) rlocus(GH) fprintf('Poles of…

Q: Compute a cc 5 truth table.

A: TRUTH TABLE: p q r p r T T T F F F T F F T T T F F T T T F F T T F T F F F T F F T…

Q: Task 1: Create the block diagram shown in Fig. 1.2 in Simulink by identifying the appro- priate…

A: Hello student Greetings Hope you are doing great. As per our policy guidelines, in case of multiple…

Q: the laminar boundary layer forms on a wedge, we can use Falkner-Skan equation. Note that quation is…

A: Hey there, I am writing the required solution of the questin mentioned above. Please do find the…

Q: et A be an mxn matrix, and B be an pXm matrix, and C be an nXp matrix. Which of the following is not…

A: According to company guidelines we are restricted to answer only first question if the other…

Q: (c) Show that (m^n) ⇒ (mVn) = T

A: Statement is stating  that the logical implication "m Λ n" implies "m V n" is always true…

Q: i Use a Karnaugh map to find a minimal sum for E = ft' + l+/zt +yzt ii. Express the Boolean…

A: Here in this question we have two parts .in the  first one we have given expression .with the help…

Q: Let C be the ternary linear code with generator matrix 1 0 0 0 2 11 0 1 0 0 1 22 0 0 1 0 201 0 0 0 1…

A: a. 0120 = [0120]b. The parity-check matrix for C is      P = [1, 0 ,0 ,1, 0, 1 ,1, 0, 1 ,1] c. The…

Q: C₁ and C₂ be two linear block codes. Define three new codes (called espectively concatenation, bar…

A: Given data, Let G and G be two linear block Codes C={(c1 c2) : c1∈C1 and c2∈ C2D={(c1 c2 +c2)…