New quantum codes from constacyclic codes over a non-chain ring

Let p be a prime of the form p=mt+1, where integers t >= 1,m >= 2 and Rm=Fp[u]/um-1. Thus, Rm is a finite commutative non-chain ring. For a given unit lambda is an element of Rm, we study lambda -constacyclic codes of length n over Rm. The necessary and sufficient conditions for these codes to contain their Euclidean duals are determined. As an application from dual-containing lambda -constacyclic codes over Rm, for m=2,3,4, we obtain many new quantum codes that improve on the known existing quantum codes.

Automated summary

In this study, lambda-cyclic codes over Rm and their Euclidean duals are investigated, leading to the discovery of new quantum codes for m=2,3,4. This research has provided insights into the properties of these codes and their improvements over existing quantum codes.