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Quantum codes from negacyclic codes over group ring (Fq+ vFq)G

İrfan Şiap, Mehmet E. Köroğlu

Published Oct 1, 2016• 0 citations
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Abstract

In this paper, we determine self dual and self orthogonal codes arising from negacyclic codes over the group ring (Fq + υFq) G. By taking a suitable Gray image of these codes we obtain many good parameter quantum error-correcting codes over Fq .

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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 .