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    Coding Theory : Linear Codes

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    Please see the attached file for the fully formatted problems.
    (a) Explain what is meant by
    (i) a linear code over Fq
    (ii) the weight w(x) of a vector x
    (iii) the weight w(C) of a code. Prove that,...

    (b) Prove that w(C) = d(C) if C is a linear code.

    (c) Define F-linear equivalence of codes. State the three row and two column operations which may be performed on generator matrices to obtain F-linearly equivalent codes, and prove that these operations do preserve F-linear equivalence.
    (d) Let C be the linear ]F3-code with generator matrix
    ....
    (1) List the codewords of C.
    (ii) Find d(C). How many errors can it detect? How many errors can it correct?
    (iii) Prove that C is a perfect code.

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    https://brainmass.com/math/discrete-math/coding-theory-linear-codes-112281

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    Let C be the linear -code with generator matrix

    Prove that C is a perfect code.

    The ...

    Solution Summary

    Linear codes are investigated.

    $2.49

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