Quantum Codes from Constacyclic Codes over the Ring F q [ u 1, u 2 ]/? u 1 2 - u 1, u 2 2 - u 2, u 1 u 2 - u 2 u 1 ?

Ahmad N. Alkenani, Mohammad Ashraf and Ghulam Mohammad
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Ahmad N. Alkenani: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Mohammad Ashraf: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Ghulam Mohammad: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Mathematics, 2020, vol. 8, issue 5, 1-11

Abstract: In this paper, we study the structural properties of ( α + u 1 β + u 2 γ + u 1 u 2 δ ) -constacyclic codes over R = F q [ u 1 , u 2 ] / 〈 u 1 2 − u 1 , u 2 2 − u 2 , u 1 u 2 − u 2 u 1 〉 where q = p m for odd prime p and m ≥ 1 . We derive the generators of constacyclic and dual constacyclic codes. We have shown that Gray image of a constacyclic code of length n is a quasi constacyclic code of length 4 n . Also we have classified all possible self dual linear codes over this ring R . We have given the applications by computing non-binary quantum codes over this ring R .

Keywords: cyclic code; constacyclic code; quantum codes; negacyclic code; Gray map (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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