Abstract
We generalize the concept of near weight stated in Carvalho et al. (IEEE Trans Inf Theory 53(5):1919---1924, 2007) in the sense that we consider maps to arbitrary well-ordered semigroups instead of the nonnegative integers. This concept can be used as a tool to study AG codes based on more than one point via elementary methods only, as well as to construct codes from higher dimensional varieties.
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