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Both texts in the other answer are great texts, and the Guruswami, Rudra, Sudan book is more based in the TCS approach to coding theory, which may be relevant to the potential reader. The books below have been split into the "mainly information theory" and "mainly coding theory" subsets. Information Theory: For mathematical rigour, the ...


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Maybe not so math oriented but with math rigor: Elements of Information Theory by Thomas M. Cover, Joy A. Thomas Essential Coding Theory by Venkatesan Guruswami, Atri Rudra and Madhu Sudan


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