Abstract
A sequence of elements from a finite field satisfies the shift and add property if the componentwise sum of any two shifts of the sequence is either a shift of the sequence or the all zero sequence. A sequence whose elements lie in an arbitrary group satisfies the shift and multiply property if the componentwise product of any two shifts of the sequence is either a shift of the sequence or the all identity sequence. The paper classifies sequences which have the shift and add property or the shift and multiply property.
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Blackburn, S.R. A Note on Sequences with the Shift and Add Property. Designs, Codes and Cryptography 9, 251–256 (1996). https://doi.org/10.1023/A:1027324404338
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DOI: https://doi.org/10.1023/A:1027324404338