H. Niederreiter

TL;DR: In this article, the authors constructed digital (t, s)-sequences in a prime-power base, where the quality parameter was defined as the least possible order of magnitude, using algebraic function fields over the finite field of order, which contained many places of degree 1 relative to the genus.

TL;DR: An in-depth analysis of the multiple-recursive matrix method for uniform pseudorandom number generation, which yields much larger period lengths than the GFSR method with the same order of the recursion and the same precision, is carried out.

TL;DR: It turns out that many good linear codes can be obtained from these generalized algebraic-geometry codes, which are based on function fields over finite fields with many places of small degree.

TL;DR: Based on a construction of Xing, Niederreiter, and Lam (see ibid, p.45, 1999), some new linear codes are found from suitable algebraic curves over finite fields that have better parameters compared with Brouwer's table.

TL;DR: It turns out that codes from two constructions of linear codes from local expansions of functions at a fixed rational point have the same bound on their parameters as Goppa's (1981) geometry codes.