Summary: The authors find justified the publication of results most of them well-known, by the use of only rudimentary notions of modern algebra making the subject accessible to the reader with limited mathematical background. The point of view is that of shift registers and error correcting codes. The most original part of the paper seems to be the use of sequences \(\{\delta_h(t)\}\) defined by \(\delta_h(t)=\binom{t+h}{h} \pmod{{\text{characteristic }k}\), in the study of linear recursive sequences whose recursion is the power of an irreducible polynomial.