Monomial Isomorphism for Tensors and Applications to Code Equivalence Problems

ePrint Report: Monomial Isomorphism for Tensors and Applications to Code Equivalence Problems

Giuseppe D'Alconzo

Starting from the problem of $d$-Tensor Isomorphism ($d$-TI), we study the relation between various Code Equivalence problems in different metrics. In particular, we show a reduction from the sum-rank metric (CE${}_{sr}$) to the rank metric (CE${}_{rk}$). To obtain this result, we investigate reductions between tensor problems. We define the Monomial Isomorphism problem for $d$-tensors ($d$-TI${}^*$ ), where, given two $d$-tensors, we ask if there are $d-1$ …

applications code eprint report metrics problem problems report result study tensor