Information on Result #1131945
Linear OOA(2172, 21848, F2, 6, 21) (dual of [(21848, 6), 130916, 22]-NRT-code), using OOA 6-folding based on linear OA(2172, 131088, F2, 21) (dual of [131088, 130916, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2172, 131090, F2, 21) (dual of [131090, 130918, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(2171, 131072, F2, 21) (dual of [131072, 130901, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2154, 131072, F2, 19) (dual of [131072, 130918, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(20) ⊂ Ce(18) [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(2172, 21848, F2, 6, 20) (dual of [(21848, 6), 130916, 21]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2173, 21848, F2, 6, 21) (dual of [(21848, 6), 130915, 22]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2174, 21848, F2, 6, 21) (dual of [(21848, 6), 130914, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(2175, 21848, F2, 6, 21) (dual of [(21848, 6), 130913, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(2172, 21848, F2, 7, 21) (dual of [(21848, 7), 152764, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(2172, 21848, F2, 8, 21) (dual of [(21848, 8), 174612, 22]-NRT-code) | [i] | ||
| 7 | Digital (151, 172, 21848)-net over F2 | [i] | ||