2134/2322 G.H. Norton G.H. Norton Ana Salagean Ana Salagean Cyclic codes and minimal strong Gröbner bases over a principal ideal ring Loughborough University 2006 untagged Information and Computing Sciences not elsewhere classified 2006-08-21 15:43:55 Journal contribution https://repository.lboro.ac.uk/articles/journal_contribution/Cyclic_codes_and_minimal_strong_Gr_bner_bases_over_a_principal_ideal_ring/9402059 We characterise minimal strong Gröbner bases of R[x] where R is a commutative principal ideal ring and deduce a structure theorem for cyclic codes of arbitary length over R. When R is an Artinian chain ring with residue field R and gcd(char(R),n) = 1, we recover a theorem for cyclic codes of length n over R due to Calderbank and Sloane for R = Z/pkZ.