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(17 citation statements)

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“…In [23], dual-containing binary codes which can be extended to a bigger code have been considered while in Corollary 11 we make no such assumption. Furthermore, in [24] it was shown that the construction provided in [23] is related to the second generalized-Hamming weights, which basically depends on the subspace property of the code, while the symbol-pair distance of the code is does not use the subspace structure and depends only on the locality properties of codewords. Hence, we feel that the two constructions are inherently different.…”

confidence: 99%

“…In [23], dual-containing binary codes which can be extended to a bigger code have been considered while in Corollary 11 we make no such assumption. Furthermore, in [24] it was shown that the construction provided in [23] is related to the second generalized-Hamming weights, which basically depends on the subspace property of the code, while the symbol-pair distance of the code is does not use the subspace structure and depends only on the locality properties of codewords. Hence, we feel that the two constructions are inherently different.…”

confidence: 99%

“…From Lemma 3.2, there exists a cyclotomic coset containing at least two consecutive integers; here it is the coset C 8 = {8, 9, 14}. Let C be the cyclic code generated by the product of the minimal polynomials C = g(x) = M (4) (x)M (8) Proof: We know that gcd(q, n) = 1. Let C be the cyclic code generated the product of the minimal polynomials M (s) (x)M (s+2) (x) .…”

confidence: 99%

“…From Lemma 3.2, there exists a cyclotomic coset containing at least two consecutive integers; here it is the coset C 8 = {8, 9, 14}. Let C be the cyclic code generated by the product of the minimal polynomials C = g(x) = M (4) (x)M (8) ] 5 code. Theorem 3.5: Let q ≥ 3 be a prime power, n > q be a prime number and consider that m = ord n (q) ≥ 2.…”

confidence: 99%

“…The several methods for constructing good families of quantum codes by numerous authors over recent years have been proposed. In [8]- [12] many binary quantum codes have been constructed by using classical error-correcting codes, such as Reed-Solomon codes, Reed-Muller codes, and algebraic-geometric codes. The theory was later extended to the nonbinary case, which authors in [13]- [15] have introduced nonbinary quantum codes for the fault-tolerant quantum computation.…”

confidence: 99%