Cyclic codes and minimal strong Gröbner bases over a principal ideal ring.
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Publication:1870034
DOI10.1016/S1071-5797(03)00003-0zbMath1040.94014OpenAlexW1996543537MaRDI QIDQ1870034
Ana Sălăgean, Graham H. Norton
Publication date: 4 May 2003
Published in: Finite Fields and their Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s1071-5797(03)00003-0
Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Principal ideal rings (13F10) Cyclic codes (94B15)
Related Items (18)
A class of constacyclic codes over ring \(R + vr\) ⋮ Dynamical Gröbner bases ⋮ The discrete multidimensional MPUM ⋮ Minimal Gröbner bases and the predictable leading monomial property ⋮ On cyclic codes over Galois rings ⋮ Repeated root cyclic codes over \(\mathbb{Z}_{p^2}+u\mathbb{Z}_{p^2}\) and their Lee distances ⋮ 1-generator quasi-cyclic codes over finite chain rings ⋮ On polycyclic codes over a finite chain ring ⋮ Lattice of ideals of the polynomial ring over a commutative chain ring ⋮ An iterative algorithm for parametrization of shortest length linear shift registers over finite chain rings ⋮ Cyclic and negacyclic codes over the Galois ring \(\text{GR}(p^2,m)\) ⋮ Repeated-root cyclic and negacyclic codes over a finite chain ring ⋮ Cyclic Codes over Galois Rings ⋮ Dual and self-dual negacyclic codes of even length over \(\mathbb Z_{2^a}\) ⋮ On the structure of 1-generator quasi-polycyclic codes over finite chain rings ⋮ APPLYING BUCHBERGER'S CRITERIA FOR COMPUTING GRÖBNER BASES OVER FINITE-CHAIN RINGS ⋮ Complete classification of \((\delta + \alpha u^2)\)-constacyclic codes of length \(p^k\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m} + u^2 \mathbb{F}_{p^m}\) ⋮ On \(\mathbb{Z}_2\mathbb{Z}_4\)-additive polycyclic codes and their Gray images
Uses Software
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