New non-binary quantum codes from skew constacyclic codes over the ring \mathbbF_p^m+v\mathbbF_p^m+v² \mathbbF_p^m

2020/10/14 by Ram Krishna Verma, Om Prakash, Verma, Ram Krishna +3
Computer Science · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.2010.07175

Abstract

In this article, we construct new non-binary quantum codes from skew constacyclic codes over finite commutative non-chain ring R= \mathbbF_p^m[v]/⟨ v³ =v ⟩ where p is an odd prime and m ≥ 1. In order to obtain such quantum codes, first we study the structural properties of skew constacyclic codes and their Euclidean duals over the ring R. Then a necessary and sufficient condition for skew constacyclic codes over R to contain their Euclidean duals is established. Finally, with the help of CSS construction and using Gray map, many new non-binary quantum codes are obtained over \mathbbF_p^m.

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