Linear transformation codes: codes with a compact description and transpoliser codes (Q2024754)

Summary: In this paper we define linear transformation codes, which provides a compact description to traditional codes. We divide them into ideal codes and multiplicative codes and show that the multiplicative codes are the more useful of the two. We relate them to linear and additive codes over non-commutative rings and show how to use the canonical orthogonals in each case to construct new codes. Extending on the specific examples of centraliser and twisted centraliser codes, we define a new family of codes, which we call transpoliser codes, that can be defined over the binary field without the restrictive upper bound on the minimum distance.