In this work, we first generalize the sigma-lcd codes over finite fields to sigma-lcd codes over finite chain rings. Under suitable conditions, linear codes over finite chain rings that are sigma-lcd codes are charact...
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In this work, we first generalize the sigma-lcd codes over finite fields to sigma-lcd codes over finite chain rings. Under suitable conditions, linear codes over finite chain rings that are sigma-lcd codes are characterized. Then we provide a necessary and sufficient condition for free constacyclic codes over finite chain rings to be sigma-lcd. We also get some new binary lcdcodes of different lengths which come from Gray images of constacyclic sigma-lcd codes over F-2+ gamma F-2+ gamma F-2(2). Finally, for special finite chain rings F-q + gamma F-q, we define a new Gray map Phi from (F-q + gamma F-q)(n) to F-q(2n), and by using sigma--lcdcodes over finite chain rings F-q + gamma F-q, we construct new entanglement-assisted quantum error-correcting (abbreviated to EAQEC) codes with maximal entanglement and parts of them are MDS EAQEC codes.
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