Information on Result #2668194
Linear OOA(2184, 1370, F2, 3, 30) (dual of [(1370, 3), 3926, 31]-NRT-code), using 21 times duplication based on linear OOA(2183, 1370, F2, 3, 30) (dual of [(1370, 3), 3927, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2183, 4110, F2, 30) (dual of [4110, 3927, 31]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2181, 4108, F2, 30) (dual of [4108, 3927, 31]-code), using
- 1 times truncation [i] based on linear OA(2182, 4109, F2, 31) (dual of [4109, 3927, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [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(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(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(30) ⊂ Ce(28) [i] based on
- 1 times truncation [i] based on linear OA(2182, 4109, F2, 31) (dual of [4109, 3927, 32]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2181, 4108, F2, 30) (dual of [4108, 3927, 31]-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(2184, 1278, F2, 4, 30) (dual of [(1278, 4), 4928, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2184, 1278, F2, 5, 30) (dual of [(1278, 5), 6206, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2184, 1278, F2, 6, 30) (dual of [(1278, 6), 7484, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(2184, 1278, F2, 7, 30) (dual of [(1278, 7), 8762, 31]-NRT-code) | [i] | ||
| 5 | Linear OOA(2184, 1278, F2, 8, 30) (dual of [(1278, 8), 10040, 31]-NRT-code) | [i] | ||
| 6 | Digital (154, 184, 1278)-net over F2 | [i] | ||