The paper uses Galois connections to study and extend generalized rank weights and extended generalized poset weights for codes and modules over rings, proving Singleton bounds, Wei-type dualities, and characterizations of optimal codes.
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Generalized Rank Weight and Extended Generalized Poset Weight Defined For Codes Over Rings: A Galois Connection Approach
The paper uses Galois connections to study and extend generalized rank weights and extended generalized poset weights for codes and modules over rings, proving Singleton bounds, Wei-type dualities, and characterizations of optimal codes.