A Note on Sequences with the Shift and Add Property
Designs, Codes and Cryptography
Error Coding for Arithmetic Processors
Error Coding for Arithmetic Processors
Shift Register Sequences
Periodicity and Correlation Properties of d-FCSR Sequences
Designs, Codes and Cryptography
Arithmetic crosscorrelations of feedback with carry shift register sequences
IEEE Transactions on Information Theory
Pseudonoise sequences based on algebraic feedback shift registers
IEEE Transactions on Information Theory
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In this paper we study various properties of arithmetic correlations of sequences. Arithmetic correlations are the with-carry analogs of classical correlations. Here we analyze the arithmetic autocorrelations of non-binary 茂戮驴-sequences, showing that they are nearly optimal. We analyze the expected auto- and cross-correlations of sequences with fixed shift. We study sequences with the arithmetic shift and add property, showing that they are exactly the 茂戮驴-sequences with prime connection element.