Linear codes Archives - IEEE Transactions on Quantum Engineering

Synchronizable Hybrid Subsystem Codes

Abstract: Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes C, D satisfying C⊥⊂C⊂D through the Calderbank-Shor-Steane (CSS) code construction. In this work, we establish connections between quantum synchronizable codes, subsystem codes, and […]

Fp -Linear and Fpm-Linear Qudit Codes From Dual-Containing Classical Codes

May 14, 2021Priya J. Nadkarni; Shayan Srinivasa GaraniOpen Access, Quantum InformationAdditives, Cascading style sheets, Encoding, Licenses, Linear codes, Quantum system, Qubit

Quantum code construction from two classical codes D1[n,k1,d1] and D2[n,k2,d2] over the field Fpm ( p is prime and m is an integer) satisfying the dual containing criteria D⊥1⊂D2 using the Calderbank–Shor–Steane (CSS) framework is well-studied. We show that the generalization of the CSS framework for qubits to qudits yields two different classes of codes, namely, the Fp -linear CSS codes and the well-known Fpm -linear CSS codes based on the […]