Lower bounds for the linear complexity of sequences over residue rings
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Binary sequences derived from ML-sequences over rings I: periods and minimal polynomials
Journal of Cryptology
Random properties of the highest level sequences of primitive sequences over Z(2e)
IEEE Transactions on Information Theory
The most significant bit of maximum-length sequences over Z2l: autocorrelation and imbalance
IEEE Transactions on Information Theory
Compression mappings on primitive sequences over Z/(pe)
IEEE Transactions on Information Theory
Injectivity of Compressing Maps on Primitive Sequences Over Z/(pe)
IEEE Transactions on Information Theory
Further Result of Compressing Maps on Primitive Sequences Modulo Odd Prime Powers
IEEE Transactions on Information Theory
The nonlinear complexity of level sequences over Z/(4)
Finite Fields and Their Applications
Compressing Mappings on Primitive Sequences over Z/(2e) and Its Galois Extension
Finite Fields and Their Applications
A new result on the distinctness of primitive sequences over Z/ (pq) modulo 2
Finite Fields and Their Applications
On the distinctness of modular reductions of primitive sequences over Z/(232-1)
Designs, Codes and Cryptography
| Hi-index | 754.84 |
Let Z/(pe) be the integer residue ring with odd prime p and integer e ≥ 2. Any sequence a over Z/(pe) has a unique p-adic expansion a = a0 + a1, ċ p+...+ae-1 ċ pe-1, where ai can be regarded as a sequence over Z/(p) for 0 ≥ i ≥ e-1. Let f(x) be a strongly primitive polynomial over Z/(pe) and a, b be two primitive sequences generated by f(x) over Z/(pe). Assume ϕ (x0, ,..., xe-1) = xe-1 + η(x0,...,xe-2) is an e-variable function over Z/(p) with the monomial p+1/2 xe-2p-1...x1p-1x0p-1 not appearing in the expression of η(x0,x1,...,xe-2). It is shown that if there exists an s ∈ Z/(p) such that ϕ(a0(t),...,ae-1(t)) = s if and only if ϕ(b0(t),...,be-1(t)) = s for all nonnegative t with α(t) ≠ 0, where α is an m-sequence determined by f(x) and a0, then a = b. This implies that for compressing sequences derived from primitive sequences generated by f(x) over Z/(pe), single element distribution is unique on all positions t with α(t) ≠ 0. In particular, when η(x0, x1,..., xe-2) = 0, it is a completion of the former result on the uniqueness of distribution of element 0 in highest level sequences.