Information on Result #2667660
Linear OOA(2149, 1370, F2, 3, 25) (dual of [(1370, 3), 3961, 26]-NRT-code), using 22 times duplication based on linear OOA(2147, 1370, F2, 3, 25) (dual of [(1370, 3), 3963, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2147, 4110, F2, 25) (dual of [4110, 3963, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2146, 4109, F2, 25) (dual of [4109, 3963, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2133, 4096, F2, 23) (dual of [4096, 3963, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(24) ⊂ Ce(22) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2146, 4109, F2, 25) (dual of [4109, 3963, 26]-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(2149, 1045, F2, 4, 25) (dual of [(1045, 4), 4031, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2149, 1045, F2, 5, 25) (dual of [(1045, 5), 5076, 26]-NRT-code) | [i] | ||
| 3 | Linear OOA(2149, 1045, F2, 6, 25) (dual of [(1045, 6), 6121, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(2149, 1045, F2, 7, 25) (dual of [(1045, 7), 7166, 26]-NRT-code) | [i] | ||
| 5 | Linear OOA(2149, 1045, F2, 8, 25) (dual of [(1045, 8), 8211, 26]-NRT-code) | [i] | ||
| 6 | Digital (124, 149, 1045)-net over F2 | [i] | ||