Information on Result #2666665
Linear OOA(2101, 21852, F2, 3, 12) (dual of [(21852, 3), 65455, 13]-NRT-code), using 21 times duplication based on linear OOA(2100, 21852, F2, 3, 12) (dual of [(21852, 3), 65456, 13]-NRT-code), using
- strength reduction [i] based on linear OOA(2100, 21852, F2, 3, 13) (dual of [(21852, 3), 65456, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2100, 65556, F2, 13) (dual of [65556, 65456, 14]-code), using
- 2 times code embedding in larger space [i] based on linear OA(298, 65554, F2, 13) (dual of [65554, 65456, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(297, 65536, F2, 13) (dual of [65536, 65439, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(281, 65536, F2, 11) (dual of [65536, 65455, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(217, 18, F2, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
- dual of repetition code with length 18 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(298, 65554, F2, 13) (dual of [65554, 65456, 14]-code), using
- OOA 3-folding [i] based on linear OA(2100, 65556, F2, 13) (dual of [65556, 65456, 14]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2101, 18325, F2, 4, 12) (dual of [(18325, 4), 73199, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2101, 18325, F2, 5, 12) (dual of [(18325, 5), 91524, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(2101, 18325, F2, 6, 12) (dual of [(18325, 6), 109849, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(2101, 18325, F2, 7, 12) (dual of [(18325, 7), 128174, 13]-NRT-code) | [i] | ||
| 5 | Linear OOA(2101, 18325, F2, 8, 12) (dual of [(18325, 8), 146499, 13]-NRT-code) | [i] | ||
| 6 | Digital (89, 101, 18325)-net over F2 | [i] | ||