Generalized weights of codes over rings and invariants of monomial ideals

On Generalized Weights for Codes over Finite Rings

We generalize the definition for higher weights for codes over rings and define weight enumerators corresponding to these weights. We give bounds for these weights and provide MacWilliams relations for the weight enumerators. We determine these weights for some codes over Z4.

New Algorithm For Computing Secondary Invariants of Invariant Rings of Monomial Groups

In this paper, a new  algorithm for computing secondary invariants of  invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBI-G basis and the standard invariants of the ideal generated by the set of primary invariants.  The advantage of the presented algorithm lies in the fact that it is well-suited to complexity analysis and very easy to i...

On generalized weights for codes over ℤk

Euclidean Weights of Codes from Elliptic Curves over Rings

We construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools, notably an estimate for certain exponential sums and some results on canonical lifts of elliptic curves. These results may be of independent interest.

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.