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**1 - 5**of**5**### Arithmetic Walsh Transform of Boolean Functions with Linear Structures

"... Abstract. Arithmetic Walsh transform(AWT) of Boolean function caugh-t our attention due to their arithmetic analogs of Walsh-Hadamard trans-form(WHT) recently. We present new results on AWT in this paper. Firstly we characterize the existence of linear structure of Boolean func-tions in terms of AWT ..."

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Abstract. Arithmetic Walsh transform(AWT) of Boolean function caugh-t our attention due to their arithmetic analogs of Walsh-Hadamard trans-form(WHT) recently. We present new results on AWT in this paper. Firstly we characterize the existence of linear structure of Boolean func-tions in terms of AWT. Secondly we show that the relation between AWT and WHT of a balanced Boolean function with a linear structure 1n is sectionally linear. Carlet and Klapper’s recent work showed that the AWT of a diagonal Boolean function can be expressed in terms of the AWT of a diagonal Boolean function of algebraic degree at most 3 in a larger number of variables.However their proof is right only when c has even weight.We complement their proof by considering the case of c with odd weight.

### nontrivial Galois ring of odd characteristic

"... of maximal period of a trinomial over ..."

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### Networked Estimation using Sparsifying Basis Prediction∗

"... We present a framework for networked state estimation, where systems encode their (possibly high dimensional) state vectors using a mutually agreed basis between the system and the estimator (in a remote monitoring unit). The basis sparsifies the state vectors, i.e., it represents them using vectors ..."

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We present a framework for networked state estimation, where systems encode their (possibly high dimensional) state vectors using a mutually agreed basis between the system and the estimator (in a remote monitoring unit). The basis sparsifies the state vectors, i.e., it represents them using vectors with few non-zero components, and as a result, the systems might need to transmit only a fraction of the original information to be able to recover the non-zero components of the transformed state vector. Hence, the estimator can recover the state vector of the system from an under-determined linear set of equations. We use a greedy search algorithm to calculate the sparsifying basis. Then, we present an upper bound for the estimation error. Finally, we demonstrate the results on a numerical example.

### On Linear Complexity of Binary Sequences Generated Using Matrix Recurrence Relation Defined Over Z 4

"... Abstract: This paper discusses the linear complexity property of binary sequences generated using matrix recurrence relation defined over Z 4. Generally algorithm to generate random number is based on recursion with seed value/values. In this paper a linear recursion sequence of matrices or vectors ..."

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Abstract: This paper discusses the linear complexity property of binary sequences generated using matrix recurrence relation defined over Z 4. Generally algorithm to generate random number is based on recursion with seed value/values. In this paper a linear recursion sequence of matrices or vectors over Z 4 is generated from which random binary sequence is obtained. It is shown that such sequences have large linear complexity.