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Questions on Coding Theory: Let C be a subspace of V (n, 2). Hence, C is a binary linear code. Let v E V(n, 2) such that v C. Consider the coset v+ C := {v+c| c E C}. (a) Prove that v+ C is not a linear code. (b) Two (arbitrary) q-ary codes C and C' that have the same length and size are distance isomorphic if there is a bijective map f from C into C'such that d(u, w) = d(f(u),f(w)) for all u, w EC. Show that C and v + C are distance isomorphic codes.

Questions on Coding Theory: Let C be a subspace of V (n, 2). Hence, C is a binary linear code. Let v E V(n, 2) such that v C. Consider the coset v+ C := {v+c| c E C}. (a) Prove that v+ C is not a linear code. (b) Two (arbitrary) q-ary codes C and C' that have the same length and size are distance isomorphic if there is a bijective map f from C into C'such that d(u, w) = d(f(u),f(w)) for all u, w EC. Show that C and v + C are distance isomorphic codes.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Questions on Coding Theory: Let C be a subspace of V (n, 2). Hence, C is a binary linear code. Let v E V(n, 2) such that v & C. Consider the coset v+ C := {v+c| c E C}. (a) Prove that v + C is not a linear code. (b) Two (arbitrary) q-ary codes C and C' that have the same length and size are distance isomorphic if there is a bijective map f from C into C'such that d(u, w) = d(f(u),f(w)) for all u, w EC. Show that C and v+ C are distance isomorphic codes.
Transcribed Image Text:Questions on Coding Theory: Let C be a subspace of V (n, 2). Hence, C is a binary linear code. Let v E V(n, 2) such that v & C. Consider the coset v+ C := {v+c| c E C}. (a) Prove that v + C is not a linear code. (b) Two (arbitrary) q-ary codes C and C' that have the same length and size are distance isomorphic if there is a bijective map f from C into C'such that d(u, w) = d(f(u),f(w)) for all u, w EC. Show that C and v+ C are distance isomorphic codes.
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