When the extension property does not hold

DOI10.1142/S0219498817500980zbMath1407.94179arXiv1512.05486MaRDI QIDQ5739068

Serhii Dyshko

Publication date: 2 June 2017

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.05486

zbMATH Keywords

general weight functionMacWilliams extension theoremsymmetrized weight compositionsocle of a modulecode over a module alphabet

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Combinatorial aspects of packing and covering (05B40) General module theory in associative algebras (16D10)

Related Items (2)

When the extension property does not hold ⋮ MacWilliams extension property for arbitrary weights on linear codes over module alphabets

Cites Work

• Two analogues of Maillet's determinant
• A generalized weight for linear codes and a Witt-MacWilliams theorems
• Character theory of finite groups
• On the equivalence of codes over finite rings
• MacWilliams' extension theorem for bi-invariant weights over finite principal ideal rings
• On the concept of code-isomorphy
• On the equivalence of codes over rings and modules
• On modules with cyclic socle
• The Extension Theorem with Respect to Symmetrized Weight Compositions
• FOUNDATIONS OF LINEAR CODES DEFINED OVER FINITE MODULES: THE EXTENSION THEOREM AND THE MACWILLIAMS IDENTITIES
• FINITE QUASI-FROBENIUS MODULES AND LINEAR CODES
• INTERSECTION GRAPH OF A MODULE
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• When the extension property does not hold
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