Self-Dual Cyclic and Quantum Codes Over Z2^{\alpha} x (Z2 + uZ2)^{\beta}
Ismail Aydogdu, Taher Abualrub
TL;DR
This paper introduces self-dual cyclic and quantum codes over a mixed algebraic structure, providing conditions for self-duality and examples of codes with good parameters, advancing coding theory in this domain.
Contribution
It establishes conditions for self-duality of Z2Z2[u]-cyclic codes and introduces quantum codes over the same structure, with practical examples.
Findings
Conditions for self-duality of Z2Z2[u]-cyclic codes
Construction of quantum codes over Z2^{eta} x (Z2 + uZ2)^{eta}
Examples of codes with good parameters
Abstract
In this paper we introduce self-dual cyclic and quantum codes over Z2^{\alpha} x (Z2 + uZ2)^{\beta}. We determine the conditions for any Z2Z2[u]-cyclic code to be self-dual, that is, C = C^{\perp}. Since the binary image of a self-orthogonal Z2Z2[u]-linear code is also a self-orthogonal binary linear code, we introduce quantum codes over Z2^{\alpha} x (Z2 + uZ2)^{\beta}. Finally, we present some examples of self-dual cyclic and quantum codes that have good parameters.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Coding theory and cryptography · Quantum-Dot Cellular Automata