Information on Result #1051704
Linear OOA(2100, 4100, F2, 4, 15) (dual of [(4100, 4), 16300, 16]-NRT-code), using OOA 4-folding based on linear OA(2100, 16400, F2, 15) (dual of [16400, 16300, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(299, 16384, F2, 15) (dual of [16384, 16285, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(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(2104, 4101, F2, 4, 15) (dual of [(4101, 4), 16300, 16]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2101, 4100, F2, 4, 15) (dual of [(4100, 4), 16299, 16]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2102, 4100, F2, 4, 15) (dual of [(4100, 4), 16298, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(2103, 4100, F2, 4, 15) (dual of [(4100, 4), 16297, 16]-NRT-code) | [i] | ||
| 5 | Linear OOA(2100, 3501, F2, 5, 15) (dual of [(3501, 5), 17405, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(2100, 3501, F2, 6, 15) (dual of [(3501, 6), 20906, 16]-NRT-code) | [i] | ||
| 7 | Linear OOA(2100, 3501, F2, 7, 15) (dual of [(3501, 7), 24407, 16]-NRT-code) | [i] | ||
| 8 | Linear OOA(2100, 3501, F2, 8, 15) (dual of [(3501, 8), 27908, 16]-NRT-code) | [i] | ||
| 9 | Digital (85, 100, 3501)-net over F2 | [i] | ||