Information on Result #2615402
Linear OOA(2189, 1376, F2, 3, 30) (dual of [(1376, 3), 3939, 31]-NRT-code), using strength reduction based on linear OOA(2189, 1376, F2, 3, 31) (dual of [(1376, 3), 3939, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2189, 4128, F2, 31) (dual of [4128, 3939, 32]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2187, 4126, F2, 31) (dual of [4126, 3939, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2187, 4126, F2, 31) (dual of [4126, 3939, 32]-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(2190, 1376, F2, 3, 30) (dual of [(1376, 3), 3938, 31]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2191, 1376, F2, 3, 30) (dual of [(1376, 3), 3937, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2189, 1376, F2, 4, 30) (dual of [(1376, 4), 5315, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2189, 1376, F2, 5, 30) (dual of [(1376, 5), 6691, 31]-NRT-code) | [i] | ||
| 5 | Linear OOA(2189, 1376, F2, 6, 30) (dual of [(1376, 6), 8067, 31]-NRT-code) | [i] | ||
| 6 | Linear OOA(2189, 1376, F2, 7, 30) (dual of [(1376, 7), 9443, 31]-NRT-code) | [i] | ||
| 7 | Linear OOA(2189, 1376, F2, 8, 30) (dual of [(1376, 8), 10819, 31]-NRT-code) | [i] | ||
| 8 | Digital (159, 189, 1376)-net over F2 | [i] | ||