2014
DOI: 10.1109/tit.2014.2298137
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Abstract: Four quantum code constructions generating several new families of good nonbinary quantum nonprimitive non-narrow-sense Bose-Chaudhuri-Hocquenghem (BCH) codes are presented in this paper. The first two ones are based on Calderbank-Shor-Steane (CSS) construction derived from two nonprimitive BCH codes, not necessarily self-orthogonal. The third one is based on nonbinary Steane's enlargement of CSS codes applied to suitable sub-families of nonprimitive non-narrow-sense BCH codes. The fourth construction is deriv… Show more

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Cited by 55 publications
(54 citation statements)
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“…These kinds of decomposition arise naturally (i.e., for the usual generators) in some families of evaluation codes as BCH codes, toric codes, J-affine variety codes, negacyclic codes, constacylic codes, etc. and the previous approach has been exploited for constructing stabilizer quantum codes, EAQECCs and LCD codes (see [7,8,9,14,17] for instance).…”
Section: 4mentioning
confidence: 99%
“…These kinds of decomposition arise naturally (i.e., for the usual generators) in some families of evaluation codes as BCH codes, toric codes, J-affine variety codes, negacyclic codes, constacylic codes, etc. and the previous approach has been exploited for constructing stabilizer quantum codes, EAQECCs and LCD codes (see [7,8,9,14,17] for instance).…”
Section: 4mentioning
confidence: 99%
“…Moreover, those with length 342 provide a great improvement with respect to the codes given in [25, Table III]. And as before, the minimum distance of our codes can be much larger than in [25].…”
Section: Examplesmentioning
confidence: 53%
“…Notice that, again, we obtain a great improvement with respect to the codes with length 124 in [25, Table III]. In addition, the minimum distance of our codes can be much larger than in [25]. Table 8 containing stabilizer codes with length 342 and 2058 (from complementary codes) over F 7 .…”
Section: Examplesmentioning
confidence: 81%
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“…More precisely, the procedure adopted in [1] does not generate codes with relatively small length with respect to large alphabets. In [8], it is possible to derive good quantum codes of minimum distance three only if the length is a prime number, whereas here we can construct codes whose lengths are not necessarily prime and with minimum distances greater than three. Further, in [6], only primitive codes were constructed.…”
Section: Examples and Code Comparisonmentioning
confidence: 99%