Tensor-Network Codes

Quantum Tensor Product Codes

Jihao Fan, ∗ Yonghui Li, † Min-Hsiu Hsieh, ‡ and Hanwu Chen 4, § School of Computer Science and Engineering, Southeast University, Nanjing, Jiangsu 211189, China School of Electrical and Information Engineering, University of Sydney, Sydney, NSW 2006, Australia Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Syd...

Twisted tensor product codes

We present two families of constacyclic linear codes with large automorphism groups. The codes are obtained from the twisted tensor product construction. AMS subject classification: 05E20, 05B25, 11T71, 94B25, 94B27, 51E22, 51E20, 20G40, 14L35

On quantum tensor product codes

On tensor products of CSS Codes

CSS codes are in one-to-one correspondance with length 3 chain complexes. The latter are naturally endowed with a tensor product ⊗ which induces a similar operation on the former. We investigate this operation, and in particular its behavior with regard to minimum distances. Given a CSS code C, we give a criterion which provides a lower bound on the minimum distance of C ⊗ D for every CSS code ...

Tensor codes for the rank metric

Linear spaces of n× n× n tensors over finite fields are investigated where the rank of every nonzero tensor in the space is bounded from below by a prescribed number μ. Such linear paces can recover any n × n × n error tensor of rank ≤ (μ−1)/2, and, as such, they can be used to correct three-way crisscross errors. Bounds on the dimensions of such spaces are given for μ ≤ 2n+1, and constructions...