A class of constacyclic BCH codes and new quantum codes

New non-binary quantum codes from constacyclic codes over <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_q[u,v]/\langle u^{2}-1, v^{2}-v, uv-vu\rangle $\end{document}</tex-math></inline-formula>

“…This quantum code has the larger minimum distance comparing with the known quantum code with parameters [ [16,8,2]] 3 appeared in [2]. = {7}, by Theorem 4.9 we get C ⊥ H ⊆ C , and Φ(C ) is a [24,20,4] linear Hermitian dual-containing code over F 5 2 . Then we obtain a new quantum code with parameters [ [24,16,4]] 5 .…”

“…Afterwards, many good quantum error-correcting codes have been constructed by using classical cyclic codes over finite fields (see Refs. [8,11,17,20,24,27]). Recently, more and more coding scholars have studied the construction of quantum codes from cyclic codes over finite rings.…”

Some Results on Images of a Class of λ-Constacyclic Codes Over Finite Fields

“…where β is a primitive 28th root of unity. The powers of β that appear in this factorization are 1,5,9,13,17,21,25, and these are union of two 5-cyclotomic cosets modulo 28. They are C 5 (1) = {1, 5, 9, 13, 17, 25} and C 5 (25) = {21}.…”

“…They can be encoded by shift registers. Recently, many coding scholars have done further research on constructing quantum codes [5], [8], [9].…”

An application of constacyclic codes to entanglement-assisted quantum MDS codes

“…As a generalization of the paper (Calderbank et al 1998), Ketkar et al (2006) defined Pauli matrices for highly states over F q and gave a way for constructing nonbinary quantum stabilizer codes from self-orthogonal additive codes over F q 2 with respect to trace-alternating form, in particular, self-orthogonal linear codes over F q 2 with respect to Hermitian inner product. Inspired by Ketkar et al (2006), many scholars have focused on construction of new nonbinary stabilizer quantum codes (Aly et al 2007;Chen et al 2015;Grassl and Rötteler 2015;He et al 2016;Hu et al 2015;Jin et al 2017;Kai and Zhu 2013;Kai et al 2014;Liqin et al 2016;Liu et al 2017;Yuan et al 2017;Zhang and Chen 2014;Zhang and Ge 2015). Brun et al (2006) developed a new systematic method for constructing QECCs.…”