Information on Result #1096076
Linear OOA(2153, 6557, F2, 5, 21) (dual of [(6557, 5), 32632, 22]-NRT-code), using OOA 5-folding based on linear OA(2153, 32785, F2, 21) (dual of [32785, 32632, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2152, 32784, F2, 21) (dual of [32784, 32632, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(2151, 32768, F2, 21) (dual of [32768, 32617, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2136, 32768, F2, 19) (dual of [32768, 32632, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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 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(2154, 6557, F2, 5, 21) (dual of [(6557, 5), 32631, 22]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2155, 6557, F2, 5, 21) (dual of [(6557, 5), 32630, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(2156, 6557, F2, 5, 21) (dual of [(6557, 5), 32629, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(2153, 5975, F2, 6, 21) (dual of [(5975, 6), 35697, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2153, 5975, F2, 7, 21) (dual of [(5975, 7), 41672, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(2153, 5975, F2, 8, 21) (dual of [(5975, 8), 47647, 22]-NRT-code) | [i] | ||
| 7 | Digital (132, 153, 5975)-net over F2 | [i] | ||