NEW QUANTUM AND LCD CODES FROM CYCLIC CODES OVER A FINITE NON-CHAIN RING.

In this work, we study cyclic codes of length n over a finite commutative non-chain ring ℛ = F q [ u , v ] / 〈 u 2 − γ u , v 2 − ϵ v , u v − v u 〉 where γ , ϵ ∈ F q * and we find new and better quantum error-correcting codes than previously known quantum error correcting codes. Then certain constraints are imposed on the generator polynomials of cyclic codes, so these codes become linear complementary dual codes (in short LCD codes). We then verify that the Gray image of linear complementary dual codes of length n over ℛ is a linear complementary dual code of length 4 n over F q by establishing a Gray map. [ABSTRACT FROM AUTHOR]