Information on Result #2668079
Linear OOA(2172, 1370, F2, 3, 29) (dual of [(1370, 3), 3938, 30]-NRT-code), using 21 times duplication based on linear OOA(2171, 1370, F2, 3, 29) (dual of [(1370, 3), 3939, 30]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2171, 4110, F2, 29) (dual of [4110, 3939, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2170, 4109, F2, 29) (dual of [4109, 3939, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2169, 4096, F2, 29) (dual of [4096, 3927, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2157, 4096, F2, 27) (dual of [4096, 3939, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(28) ⊂ Ce(26) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2170, 4109, F2, 29) (dual of [4109, 3939, 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(2172, 1067, F2, 4, 29) (dual of [(1067, 4), 4096, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2172, 1067, F2, 5, 29) (dual of [(1067, 5), 5163, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(2172, 1067, F2, 6, 29) (dual of [(1067, 6), 6230, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(2172, 1067, F2, 7, 29) (dual of [(1067, 7), 7297, 30]-NRT-code) | [i] | ||
| 5 | Linear OOA(2172, 1067, F2, 8, 29) (dual of [(1067, 8), 8364, 30]-NRT-code) | [i] | ||
| 6 | Digital (143, 172, 1067)-net over F2 | [i] | ||