Information on Result #1052117
Linear OOA(2129, 4100, F2, 4, 18) (dual of [(4100, 4), 16271, 19]-NRT-code), using OOA 4-folding based on linear OA(2129, 16400, F2, 18) (dual of [16400, 16271, 19]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2127, 16398, F2, 18) (dual of [16398, 16271, 19]-code), using
- 1 times truncation [i] based on linear OA(2128, 16399, F2, 19) (dual of [16399, 16271, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2127, 16384, F2, 19) (dual of [16384, 16257, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2113, 16384, F2, 17) (dual of [16384, 16271, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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 X applied to Ce(18) ⊂ Ce(16) [i] based on
- 1 times truncation [i] based on linear OA(2128, 16399, F2, 19) (dual of [16399, 16271, 20]-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(2130, 4100, F2, 4, 18) (dual of [(4100, 4), 16270, 19]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2131, 4100, F2, 4, 18) (dual of [(4100, 4), 16269, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2129, 4100, F2, 5, 18) (dual of [(4100, 5), 20371, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2129, 4100, F2, 6, 18) (dual of [(4100, 6), 24471, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(2129, 4100, F2, 7, 18) (dual of [(4100, 7), 28571, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(2129, 4100, F2, 8, 18) (dual of [(4100, 8), 32671, 19]-NRT-code) | [i] | ||
| 7 | Digital (111, 129, 4100)-net over F2 | [i] | ||