Tate's algorithm tells us that for an elliptic curve E over a local field K of residue characteristic ≥5, E / K has potentially good reduction if and only if ord ( j E ) ≥ 0 . It also tells us that when E / K is semistable the dual graph of the special fibre of the minimal regular model of E / K unr can be recovered from ord ( j E ) . We generalise these results to hyperelliptic curves of genus g ≥ 2 over local fields of odd residue characteristic K by defining a list of absolute invariants that determine the potential stable model of a genus g hyperelliptic curve C . They also determine the dual graph of the special fibre of the minimal regular model of C / K unr if C / K is semistable. This list depends only on the genus of C , and the absolute invariants can be written in terms of the coefficients of a Weierstrass equation for C . We explicitly describe the method by which the valuations of the invariants recover the dual graphs. Additionally, we show by way of a counterexample that if g ≥ 2 , there is no list of invariants whose valuations determine the dual graph of the special fibre of the minimal regular model of a genus g hyperelliptic curve C over a local field K of odd residue characteristic when C is not assumed to be semistable.

Sum-rank metric codes have recently attracted the attention of many researchers, due to their relevance in several applications. Mathematically, the sum-rank metric is a natural generalization of both the Hamming metric and the rank metric. In this paper, we provide an Anticode Bound for the sum-rank metric, which extends the corresponding Hamming and rank-metric Anticode bounds. We classify then optimal anticodes, i.e., codes attaining the sum-rank metric Anticode Bound. We use these optimal anticodes to define generalized sum-rank weights and we study their main properties. In particular, we prove that the generalized weights of an MSRD code are determined by its parameters. As an application, in the Appendix we explain how generalized weights measure information leakage in multishot network coding.