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Let C be the binary code {(0,0, 1), (1, 1, 1), (1, 0, 0), (0, 1, 0)}. a.) Show that C is not linear. b.) What is the minimum distance of C? (Hint: since C is not minimum weight among the codewords.) c.) Show that C satisfies the Singleton bound with equality.

Let C be the binary code {(0,0, 1), (1, 1, 1), (1, 0, 0), (0, 1, 0)}. a.) Show that C is not linear. b.) What is the minimum distance of C? (Hint: since C is not minimum weight among the codewords.) c.) Show that C satisfies the Singleton bound with equality.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let C be the binary code {(0, 0, 1), (1, 1, 1), (1, 0, 0), (0, 1, 0)}. a.) Show that C is not linear. b.) What is the minimum distance of C? (Hint: since C is not minimum weight among the codewords.) c.) Show that C satisfies the Singleton bound with equality.
Transcribed Image Text:Let C be the binary code {(0, 0, 1), (1, 1, 1), (1, 0, 0), (0, 1, 0)}. a.) Show that C is not linear. b.) What is the minimum distance of C? (Hint: since C is not minimum weight among the codewords.) c.) Show that C satisfies the Singleton bound with equality.
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