Information on Result #1051487
Linear OOA(286, 4100, F2, 4, 13) (dual of [(4100, 4), 16314, 14]-NRT-code), using OOA 4-folding based on linear OA(286, 16400, F2, 13) (dual of [16400, 16314, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(285, 16384, F2, 13) (dual of [16384, 16299, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(271, 16384, F2, 11) (dual of [16384, 16313, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(215, 16, F2, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
- dual of repetition code with length 16 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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
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(290, 4101, F2, 4, 13) (dual of [(4101, 4), 16314, 14]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(287, 4100, F2, 4, 13) (dual of [(4100, 4), 16313, 14]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(288, 4100, F2, 4, 13) (dual of [(4100, 4), 16312, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(289, 4100, F2, 4, 13) (dual of [(4100, 4), 16311, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(286, 4100, F2, 5, 13) (dual of [(4100, 5), 20414, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(286, 4100, F2, 6, 13) (dual of [(4100, 6), 24514, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(286, 4100, F2, 7, 13) (dual of [(4100, 7), 28614, 14]-NRT-code) | [i] | ||
| 8 | Linear OOA(286, 4100, F2, 8, 13) (dual of [(4100, 8), 32714, 14]-NRT-code) | [i] | ||
| 9 | Digital (73, 86, 4100)-net over F2 | [i] | ||