A construction of digital (0,s)-sequences involving finite-row generator matrices

This paper presents a generalization of a construction method for digital (0,s)-sequences over Fq introduced by Niederreiter which is based on hyperderivatives of polynomials over Fq. Within this generalized concept, we are able to introduce direct constructions of finite-row digital (0,s)-sequences over arbitrary finite fields Fq for arbitrary dimensions s⩽q. Previously, explicit examples of finite-row digital (0,s)-sequences have been known only for finite prime fields and for specific chosen dimensions. Further, this method furnishes additional insights into the structure of finite-row digital (0,s)-sequences and their generator matrices, and this approach permits shorter proofs for earlier interesting results on these sequences.