Information on Result #806645
Linear OOA(2100, 260, F2, 2, 22) (dual of [(260, 2), 420, 23]-NRT-code), using OOA 2-folding based on linear OA(2100, 520, F2, 22) (dual of [520, 420, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2100, 521, F2, 22) (dual of [521, 421, 23]-code), using
- 1 times truncation [i] based on linear OA(2101, 522, F2, 23) (dual of [522, 421, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2100, 512, F2, 23) (dual of [512, 412, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(291, 512, F2, 21) (dual of [512, 421, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 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(22) ⊂ Ce(20) [i] based on
- 1 times truncation [i] based on linear OA(2101, 522, F2, 23) (dual of [522, 421, 24]-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(2100, 257, F2, 3, 22) (dual of [(257, 3), 671, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2100, 257, F2, 4, 22) (dual of [(257, 4), 928, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(2100, 257, F2, 5, 22) (dual of [(257, 5), 1185, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(2100, 257, F2, 6, 22) (dual of [(257, 6), 1442, 23]-NRT-code) | [i] | ||
| 5 | Linear OOA(2100, 257, F2, 7, 22) (dual of [(257, 7), 1699, 23]-NRT-code) | [i] | ||
| 6 | Linear OOA(2100, 257, F2, 8, 22) (dual of [(257, 8), 1956, 23]-NRT-code) | [i] | ||
| 7 | Digital (78, 100, 257)-net over F2 | [i] | ||