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This is a Quantitative Study study.

October 12, 2025Open Access

Bounds and MacWilliams Identities for codes over Artinian rings

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New relations between code type and dual free rank highlighted, contributing to our understanding of dual codes.
Upper bounds for Hamming distance derived from code length and type, offering new insights and applications.
Application of Nagata idealizations to connect results with Frobenius rings expands coding theory's methodologies.
Conceptually new weight enumerator polynomial introduced, applicable in varying contexts, including infinite rings.

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Analysis establishes new relations for linear codes and their duals, suggesting implications for coding theory.

Camps-Moreno et al. (2025) studied this question.

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