Two Families of Quantum Codes Derived from Cyclic Codes
Kenza Guenda
TL;DR
This paper characterizes affine-invariant cyclic codes and introduces new quantum codes derived from classical cyclic and duadic codes, addressing open problems in quantum coding theory.
Contribution
It provides a characterization of affine-invariant cyclic codes and constructs new families of quantum codes from classical codes, including solutions to open problems.
Findings
Derived a family of pure quantum codes using CSS construction
Introduced a new family of degenerate quantum codes from duadic codes
Characterized affine-invariant maximal extended cyclic codes
Abstract
We characterize the affine-invariant maximal extended cyclic codes. Then by the CSS construction, we derive from these codes a family of pure quantum codes. Also for ordnq even, a new family of degenerate quantum stabilizer codes is derived from the classical duadic codes. This answer an open problem asked by Aly et al.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Coding theory and cryptography