New QEC and EAQEC codes from repeated-root cyclic codes of length \(10p^s\) over finite fields \(\mathbb {F}_{p^m}\)

Let p be an odd prime with \(p\ne 5\) $p\ne 5$ . In this paper, we first provide the structures of repeated-root cyclic codes of length \(10p^s\) $10p^s$ over finite fields \(\mathbb {F}_{p^m}\) ${\mathbb{F}}_{p^m}$ . We then give two methods of constructing good quantum error-correcting (QEC) codes from repeated-root cyclic codes of length \(10p^s\) $10p^s$ over finite fields \(\mathbb {F}_{p^m}\) ${\mathbb{F}}_{p^m}$ . By means of the dimensions of repeated-root cyclic codes of length \(10p^s\) $10p^s$ over finite fields \(\mathbb {F}_{p^m}\) ${\mathbb{F}}_{p^m}$ , we exhibit an effective manner for constructing new EAQEC codes. We show that the usage of these methods brings us many good QEC and EQAEC codes having these advantages: (1) the parameters of our QEC and EQAEC codes are different from all the previous constructions; (2) for repeated-root cyclic codes, our methods allows for easily calculating the dimensions of QEC and EQAEC codes, and the numbers c of pre-shared maximally entangled states of EAQEC codes.