A Note on Sequences with the Shift and Add Property

Authors:
S. R. Blackburn
Affiliations:
Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
Venue:
Designs, Codes and Cryptography
Year:
1996

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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.