Year: 2026
Type: preprint
Abstract: LCD codes over finite commutative chain rings are known to be free. However, if the ring is not indecomposable, there always exists an LCD ideal that is projective but not free. We prove that all two-sided LCD codes are projective. We generalise the characterisation of finite commutative Frobenius rings by means of the size condition of a code and its dual to the noncommutative setting. This result is applied to prove that group codes are LCD if and only if they are generated by a central idempotent.
Source: arXiv (Cornell University)
Author: Krasula, Dominik
Institution: Charles University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3893806229
OpenAlex ID: W7213320487