Polynomial remainder codes are a large class of codes derived from the Chinese re-mainder theorem that includes Reed-Solomon codes as a special case. In this paper, we revisit these codes and study them more carefully than in previous work. We explicitly allow the code symbols to be polynomials

It is known that when the blocklengths of two cycljc codes are relatively prime their product code is cyclic when serialized using Chinese Remainder Theorem. When the blocklengths are equal we characterize product codes that are cyclic when serialized either rowwise or columnwise. SUMMARY Given two

We prove that self-dual codes exist over all finite commutative Frobenius rings, via their decomposition by the Chinese Remainder Theorem into local rings. We construct non-free self-dual codes under some conditions, using self-dual codes over finite fields, and we also construct free self

dynamical processes, among others. Thus, it is important to blend ideas from information theory and control theory to address problems at the core of such distributed systems. This dissertation looks at communication scenarios, in which there are feedback channels available for enhancing communication

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full data exchange, i.e., each user in a cluster wants to learn the messages of all the other users in the same cluster. Novel signal alignment techniques are developed to systematically construct the beamforming matrices at the users and the relay for efficient physical-layer network coding. Based

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beamforming design at the users and at the relay is proposed to align signals for efficient implementation of physical-layer network coding (PNC). It is shown that, when the user number K = 3, the proposed beamforming design can achieve the DoF capacity of the considered mRC for any (M,N) setups

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the solution of inde nite systems arising in nonlinear