Background on Information Theory and Coding Theory
This chapter summarizing background information assumes that the reader has some familiarity with linear algebra and basic probability. The basic model of information theory and error-correcting block codes is introduced. The basic example of the Hamming [7,4,3] code is presented in detail.
What is ironic is that even in basic background issues, coding theory has interesting open questions. For example, for a given length and dimension, which code is the best 2-error-correcting code? Another example: see Manin’s theorem 19 and the closely related Conjecture 22 below.
KeywordsLinear Code Cyclic Code Asymptotic Bound Cyclic Shift Quadratic Residue
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