Generalized rank weights and extended generalized poset weights for codes over rings form Galois connections, yielding unified Wei-type duality theorems and Singleton-type bounds that subsume prior results for fields and Galois rings.
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Generalized Rank Weight and Extended Generalized Poset Weight Defined For Codes Over Rings: A Galois Connection Approach
Generalized rank weights and extended generalized poset weights for codes over rings form Galois connections, yielding unified Wei-type duality theorems and Singleton-type bounds that subsume prior results for fields and Galois rings.