True or False: It is impossible to find a binary linear code with block length N=16, dimension k=9, and minimum distance d=5. If true provide a proof, if false provide a counterexample.
FALSE
the condition for binary linear code
N - K + 1 >=d
16 - 9 + 1 = 8>=5
hence it is possible to find a binary linear code
True or False: It is impossible to find a binary linear code with block length N=16,...
If C is a subspace of , prove that . (C is a binary linear code with length n and dimension k, is the dual code of C) F dim(C) dim(C)= n We were unable to transcribe this image
True or false: If N is a subgroup of a group G then the set of
left cosets of N in G form a group by defining aN bN = abN for all
left cosets aN and bN. Give a proof or a counterexample.
(b) (5 points) True or false: If N is a subgroup of a group G then the set of left cosets of N in G form a group by defining aNbN abN for all left cosets...
Let C' be a binary code of length n and distance d 2t +1. Prove that 2"
Let C' be a binary code of length n and distance d 2t +1. Prove that 2"
Question 9. Let (A-) be a binary structure. When the book defined identity, it meant 2 sided identity, but it is also possible to talk about one sided (right and left) identities. Come up with a reasonable definition of the terms: left identity (denoted by ez) and right identity denoted by eR). (a) Is it true that, if a left (respectively, right) identity exists, then it is unique? If it is true, prove it; if it is false, provide a...
(9) True of False: For all (n xn) matrices A and B, dim(ker(AB)) > dim(ker(B)). (That is, the dimension of the nullspace or kernel of AB is at least as big as the dimension of the nullspace or kernel of B.) Justify your answer. (10) (Extra Credit) Let A be any nxn matrix. If n is odd, prove that it is impossible for im(A) = (A).
128289 Computer Science
Q1. True or False? O(n) is called linear time 02. True or False? O(n*n) is called quadratic time 03. True or False? An algorithm that has complexity O(log n) is always faster than one that has O(n) complexity. 04. What is the output of the below code: int main() int arrl5] 1,2,34,5) cout< arr[5] Q5. Arrange these time complexities from low to high
4. H ere are some True/False questions. If your answer is "TRUE", there is no need to justify your answer. If your answer is "FALSE", then you should justity your answer with a counterexample or explanation. There are also some "short-answer" questions. . A. (True-False). Every simple field extension of K is a finite field extension. . B. (True-False). Let R⑥ F be a field extension. Suppose that F is a of u E F, and splitting field for the...
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The following problem is to design an algorithm which check if a binary tree is a binary search tree. The following code was given. There exists a bug in this code for the variable last printed. (20 points) 6. Find the bug and provide a way to fix this bug: public static Integer last printed-null: public static boolean checkBST (TreeNode n) if (nnull) return true // check/ recurse left if (checkBST (n.left)) return false; /I check current...
help please and thank you
5. True or False. For each of the following statements, determine whether the statement is True or False and then prove your assertion. That is, for each True statement provide a proof, and for each False statement provide a counterexample (with explanation). Hint: Draw appropriate Venn diagrams to aid your explorations! Let A, B and C be sets (a) A - (B C) (A - B) C (b) (А — В) — С - (А-С)...
1. (30 points) Consider the systematic binary linear (6,3) code with generator matrix 1 0 01 1 0 G- 0 1 0 0 1 1 a) Determine the parity check matrix H of the code. b) What is the minimum distance of the code? How many errors can this code correct and detect? c) Show the results in b) using decoding table d) Find the most likely codeword, given that the noisy received codeword is 010101. e) Now suppose 001101...