On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes

Betti numbers of Stanley–Reisner rings with pure resolutions

Let ∆ be simplicial complex and let k[∆] denote the Stanley– Reisner ring corresponding to ∆. Suppose that k[∆] has a pure free resolution. Then we describe the Betti numbers and the Hilbert– Samuel multiplicity of k[∆] in terms of the h–vector of ∆. As an application, we derive a linear equation system and some inequalities for the components of the h–vector of the clique complex of an arbitra...

Generalized Reed-Muller codes over Galois rings

Recently, Bhaintwal and Wasan studied the Generalized Reed-Muller codes over the prime power integer residue ring. In this paper, we give a generalization of these codes to Generalized Reed-Muller codes over Galois rings.

Hilbert regularity of Stanley-Reisner rings

On the Reed-Muller codes

We give a brief but complete account of all the essential facts concerning the Reed-Muller and punctured Reed-Muller codes. The treatment is new and includes an easy, direct proof of the fact that the punctured Reed-Muller codes are the codes of the projective geometries over the binary eld. We also establish the existence of two short exact sequences that lead to new proofs that the minimum-we...

Combinatorial Invariance of Stanley-reisner Rings

In this short note we show that Stanley-Reisner rings of simplicial complexes, which have had a ‘dramatic application’ in combinatorics [2, p. 41] possess a rigidity property in the sense that they determine their underlying simplicial complexes. For the readers convenience we recall the notion of a Stanley-Reisner ring (for more information the reader is referred to [1, Ch. 5]). Let V be a fin...