Two approaches to the extension problem for arbitrary weights over finite module alphabets

The extension problem underlies notions of code equivalence. Two approaches to the extension problem are described. One is a matrix approach that reduces the general problem for weights to one for symmetrized weight compositions. The other is a monoid algebra approach that reframes the extension problem in terms of modules over the monoid algebra determined by the multiplicative monoid of a finite ring. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.