Properties of the output sequence of a simplest 2-linear shift register over \(\mathbb Z_{2^{n}}\). (English. Russian original) Zbl 1278.94040
Discrete Math. Appl. 17, No. 6, 539-566 (2007); translation from Diskretn. Mat. 19, No. 4, 70-96 (2007).
Summary: The output sequence of a simplest self-controlled 2-linear shift register over the residue ring \(R = \mathbb Z_{2^n}\) is considered. For a fixed output function we study the rank and the period of the output sequence. In some special cases frequency characteristics of cycles of the first coordinate sequence of the output sequence are considered. It is shown that the rank of the output sequence of the 2-dimensional shift register is much greater than the rank of the output sequence of a 1-dimensional register of the same length.
MSC:
| 94A55 | Shift register sequences and sequences over finite alphabets in information and communication theory |
| 11T71 | Algebraic coding theory; cryptography (number-theoretic aspects) |
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