Generalized explicit inversive generators of small p -weight degree

Generalized explicit inversive generators of small p-weight degree

Period Distribution of Inversive Pseudorandom Number Generators Over Galois Rings

In 2009, Solé and Zinoviev (Eur. J. Combin., vol. 30, no. 2, pp. 458-467, 2009) proposed an open problem of arithmetic interest to study the period of the inversive pseudorandom number generators (IPRNGs) and to give conditions bearing on a, b to achieve maximal period, we focus on resolving this open problem. In this paper, the period distribution of the IPRNGs over the Galois ring (Zpe ,+,×) ...

Minimum-weight odewords as generators of generalized Reed-Muller odes

Minimum-weight codewords as generators of generalized Reed-Muller codes

We establish the range of values of ρ, where 0 ≤ ρ ≤ m(q − 1), for which the generalized Reed-Muller code RFq (ρ,m) of length q over the field Fq of order q is spanned by its minimum-weight vectors.

Period Distribution of Inversive Pseudorandom Number Generators Over Finite Fields

In this paper, we focus on analyzing the period distribution of the inversive pseudorandom number generators (IPRNGs) over finite field (ZN ,+,×), where N > 3 is a prime. The sequences generated by the IPRNGs are transformed to 2-dimensional linear feedback shift register (LFSR) sequences. By employing the generating function method and the finite field theory, the period distribution is obtain...