Metrics that respect the support
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In this work we explore the family of metrics determined by S-weights, i.e., non-negative functions over finite fields that respect the support. First, we introduce a conditional sum of weights and classify those which every set of equivalent weights is closed under such sums. Then, we introduce an structure to represent all decision criteria which allows us to characterize the group of linear isometries for S-weights sharing the same equivalence class regarding the decoding criterion.
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