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.