Information on Result #1131442
Linear OOA(2138, 21848, F2, 6, 17) (dual of [(21848, 6), 130950, 18]-NRT-code), using OOA 6-folding based on linear OA(2138, 131088, F2, 17) (dual of [131088, 130950, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2138, 131090, F2, 17) (dual of [131090, 130952, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2137, 131072, F2, 17) (dual of [131072, 130935, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2120, 131072, F2, 15) (dual of [131072, 130952, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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 X applied to Ce(16) ⊂ Ce(14) [i] based on
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(2138, 21848, F2, 6, 16) (dual of [(21848, 6), 130950, 17]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2139, 21848, F2, 6, 17) (dual of [(21848, 6), 130949, 18]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2140, 21848, F2, 6, 17) (dual of [(21848, 6), 130948, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(2138, 21848, F2, 7, 17) (dual of [(21848, 7), 152798, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2138, 21848, F2, 8, 17) (dual of [(21848, 8), 174646, 18]-NRT-code) | [i] | ||
| 6 | Digital (121, 138, 21848)-net over F2 | [i] | ||