A Note on Sequences with the Shift and Add Property
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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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- 1.Guang Gong, Adina Di Porto and William Wolfowicz, Performance Testing of Galois Linear Group Sequences, Proceedings of SPRC '93, Rome, Italy, (1993) pp. 90–105.Google Scholar
- 2.Rudolf Lidl and Harald Niederreiter, Introduction to Finite Fields and their Applications (Revised Edition), Cambridge University Press, Cambridge (1994).Google Scholar
- 3.Joseph J. Rotman An Introduction to the Theory of Groups (3rd Edition), Wm. C. Brown, Dubuque, 1988.Google Scholar
- 4.Rainer A. Rueppel, Analysis and Design of Stream Ciphers, Springer-Verlag, Berlin-Heidelberg (1986).Google Scholar
- 5.Neal Zierler, Linear Recurring Sequences, J. Soc. Indust. Appl. Math., Vol. 7, No. 1, (1959) pp. 31–48.Google Scholar