Cyclic codes and minimal strong Gröbner bases over a principal ideal ring
G.H. Norton
Ana Salagean
2134/2322
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.
2006-08-21 15:43:55
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Information and Computing Sciences not elsewhere classified