Weak Composition Lattices and Ring-Linear Anticodes
Abstract
Lattices and partially ordered sets have played an increasingly important role in coding theory, providing combinatorial frameworks for studying structural and algebraic properties of error-correcting codes. Motivated by recent works connecting lattice theory, anticodes, and coding-theoretic invariants, we investigate ring-linear codes endowed with the Lee metric. We introduce and characterize optimal Lee-metric anticodes over the ring . We show that the family of such anticodes admits a natural partition into subtypes and forms a lattice under inclusion. We establish a bijection between this lattice and a lattice of weak compositions ordered by dominance. As an application, we use this correspondence to introduce new invariants for Lee-metric codes via an anticode approach.
Keywords
Cite
@article{arxiv.2601.07725,
title = {Weak Composition Lattices and Ring-Linear Anticodes},
author = {Jessica Bariffi and Drisana Bhatia and Giuseppe Cotardo and Violetta Weger},
journal= {arXiv preprint arXiv:2601.07725},
year = {2026}
}