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On the other hand, when a quantum code is pure we can easily obtain uniform states. In fact, from Theorem 1 to Theorem 9 we always make quantum codes by using uniform states generated by orthogonal partitions. A link between an IrOA and the uniform state is established by Connection 1. The third is that for the constructed QECCs, their every basis state has less than or equal to terms compared with the existing binary QECCs in. The second is that Theorems 1 and 7–9 can be generalized to construct QECCs ( ( N, K, d ) ) q for arbitrary d and a prime power q. The first is to be able to construct an ( ( N, K 1, d ) ) QECC from each ( ( N, K, d ) ) QECC we construct for arbitrary integer 1 ≤ K 1 ≤ K. Several methods for constructing QECCs from OAs are presented. In the work, by using OAs, we study the relation between uniform states and binary QECCs. For example, the code ( ( 4, 4, 2 ) ) in Example 1 after it is normalized is the same as the one constructed using the method proposed in. The amplitudes in the superposition for each logical codeword are all equal to m K. An r × N array A with entries from a set S =. Orthogonal arrays (OAs) play a more and more important role in quantum information theory.
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The main goal of this work is to link between orthogonal arrays and binary QECCs and to construct more families of new codes. However, the majority of binary QECCs constructed so far are stabilizer codes. Some other constructions of non-stabilizer codes, such as CWS codes, the codes in, and permutation-invariant codes such as in have been studied. Based on this characterization, they derived a method to construct pure p-ary quantum codes with dimensions not necessarily equal to powers of p. Feng and Xing presented a characterization of (binary and non-binary) quantum codes. Li and Li obtained quantum codes of minimum distance three which are optimal or near optimal, and some quantum codes of minimum distance four which are better than previously known codes. Feng and Ma made a way to obtain good pure stabilizer quantum codes, binary or nonbinary. In recent years, the research on QECCs especially on binary QECCs has made great progress. provided a close connection between QECCs and classical error correction codes, which leads to constructing QECCs from known classical error correction codes. In 1995, Shor gave the simplest quantum simulation of a classical coding plan and then constructed the first QECC. Errors are inevitable in quantum information processing, so quantum error-correcting codes (QECCs) are very important for quantum communication and quantum computing.