Abstract
Partially ordered sets is a central concept in set theory (hence in many branches of mathematics) and a subject of study on its own. In the context of coding theory it appears as an auxiliary structure that allows to determine different metrics over \(\mathbb {F}_{q}^{n}\), metrics that satisfy the conditions stated at the end Sect. 1.1: they assume only integer values, are determined by a weight and respect the support of vectors. As we shall see, many properties concerning the metrics can be derived from properties of the poset.
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Firer, M., S. Alves, M.M., Pinheiro, J.A., Panek, L. (2018). Poset Metrics. In: Poset Codes: Partial Orders, Metrics and Coding Theory. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-93821-9_2
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DOI: https://doi.org/10.1007/978-3-319-93821-9_2
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