Information on Result #1132647
Linear OOA(2251, 21855, F2, 6, 28) (dual of [(21855, 6), 130879, 29]-NRT-code), using OOA 6-folding based on linear OA(2251, 131130, F2, 28) (dual of [131130, 130879, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2251, 131135, F2, 28) (dual of [131135, 130884, 29]-code), using
- 1 times truncation [i] based on linear OA(2252, 131136, F2, 29) (dual of [131136, 130884, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- linear OA(2239, 131072, F2, 29) (dual of [131072, 130833, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2188, 131072, F2, 23) (dual of [131072, 130884, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(213, 64, F2, 5) (dual of [64, 51, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2252, 131136, F2, 29) (dual of [131136, 130884, 30]-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(2251, 21855, F2, 7, 28) (dual of [(21855, 7), 152734, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2251, 21855, F2, 8, 28) (dual of [(21855, 8), 174589, 29]-NRT-code) | [i] | ||
| 3 | Digital (223, 251, 21855)-net over F2 | [i] | ||