Linear Codes and Polylinear Recurrences over Finite Rings and Modules (A Survey)

Code equivalence characterizes finite Frobenius rings

“…Kurakin et al [8] first introduced such codes for alphabets that are modules over a finite commutative ring. Later, Greferath et al [5] developed the theory for modules over an arbitrary finite ring.…”

On repeated-root multivariable codes over a finite chain ring

“…Proof The result is a consequence of[15, Theorem 4.3] and[8, Proposition 5]. Namely, sinceK R, there existsK R[X 1 , .…”

Arcs in projective Hjelmslev planes

“…This theory can be viewed as a natural generalisation of the theory of linear codes over finite fields. In the commutative case, it is a part of the more generally theory of linear codes over quasi-Frobenius modules (see [1,2,3,10]). …”

“…Formerly all except a few authors were only interested in codes over Z 4 , but nowadays an increasing number of research papers deals with linear codes over other finite rings and modules (see [l]- [9], and, in particular, the survey [10]). …”