Information on Result #1679844
Linear OOA(2100, 4100, F2, 7, 14) (dual of [(4100, 7), 28600, 15]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2100, 4100, F2, 4, 14) (dual of [(4100, 4), 16300, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2100, 16400, F2, 14) (dual of [16400, 16300, 15]-code), using
- strength reduction [i] 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
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- strength reduction [i] based on linear OA(2100, 16400, F2, 15) (dual of [16400, 16300, 16]-code), using
Mode: 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, 4100, F2, 7, 14) (dual of [(4100, 7), 28599, 15]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2100, 4099, F2, 8, 14) (dual of [(4099, 8), 32692, 15]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 3 | Linear OOA(2100, 4099, F2, 21, 14) (dual of [(4099, 21), 85979, 15]-NRT-code) | [i] | ||