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- W3000207348 abstract "In this work we explore a family of metrics over a finite field Fq which respect the support of vectors. We show how these metrics can be obtained from the edge-labeled Hamming cube and, based on this representation, we give a description of the group of linear isometries (for q > 2). Next, we introduce the concept of conditional sum of metrics and determine what are the conditions that, out of two metrics respecting the support, give rise to a new such metric. Finally, we introduce the labeled-poset block metrics, a new family of metrics which respects support of vectors, filling a gap existing in the known universe of such metrics. For this family, we give a full description of the group of linear isometries and determine sufficient conditions to ensure the existence of a MacWilliams' identity." @default.
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- W3000207348 date "2020-06-01" @default.
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- W3000207348 title "Weights Which Respect Support and NN-Decoding" @default.
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- W3000207348 doi "https://doi.org/10.1109/tit.2020.2966997" @default.
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