Weak Composition Lattices and Ring-Linear Anticodes
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915723728650240 |
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| author | Bariffi, Jessica Bhatia, Drisana Cotardo, Giuseppe Weger, Violetta |
| author_facet | Bariffi, Jessica Bhatia, Drisana Cotardo, Giuseppe Weger, Violetta |
| contents | 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 $\mathbb{Z}/p^s\mathbb{Z}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07725 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak Composition Lattices and Ring-Linear Anticodes Bariffi, Jessica Bhatia, Drisana Cotardo, Giuseppe Weger, Violetta Information Theory 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 $\mathbb{Z}/p^s\mathbb{Z}$. 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. |
| title | Weak Composition Lattices and Ring-Linear Anticodes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.07725 |