Abstract Algebra: Theory and Applications · Problem 8.6.6

Isomorphisms — Thomas Judson

Mathematics — Abstract Algebra · minimum-distance

Problem

In each of the following codes, what is the minimum distance for the code? What is the best situation we might hope for in connection with error detection and error correction? ((a)) (011010)(011010) (011100)(011100) (110111)(110111) (110000)(110000) ((b)) (011100)(011100) (011011)(011011) (111011)(111011) (100011)(100011) (000000)(000000) (010101)(010101) (110100)(110100) (110011)(110011) ((c)) (000000)(000000) (011100)(011100) (110101)(110101) (110001)(110001) ((d)) (0110110)(0110110) (0111100)(0111100) (1110000)(1110000) (1111111)(1111111) (1001001)(1001001) (1000011)(1000011) (0001111)(0001111) (0000000)(0000000) Hint. (a) dmin⁡=2d_{\min} = 2; (c) dmin⁡=1d_{\min} = 1.

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