Information on Result #947688
Linear OOA(2219, 1382, F2, 3, 35) (dual of [(1382, 3), 3927, 36]-NRT-code), using OOA 3-folding based on linear OA(2219, 4146, F2, 35) (dual of [4146, 3927, 36]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2217, 4144, F2, 35) (dual of [4144, 3927, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
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(2219, 1382, F2, 3, 34) (dual of [(1382, 3), 3927, 35]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2220, 1382, F2, 3, 35) (dual of [(1382, 3), 3926, 36]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2221, 1382, F2, 3, 35) (dual of [(1382, 3), 3925, 36]-NRT-code) | [i] | ||
| 4 | Linear OOA(2218, 1381, F2, 3, 34) (dual of [(1381, 3), 3925, 35]-NRT-code) | [i] | Truncation for OOAs | |
| 5 | Linear OOA(2219, 1382, F2, 4, 35) (dual of [(1382, 4), 5309, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(2219, 1382, F2, 5, 35) (dual of [(1382, 5), 6691, 36]-NRT-code) | [i] | ||
| 7 | Linear OOA(2219, 1382, F2, 6, 35) (dual of [(1382, 6), 8073, 36]-NRT-code) | [i] | ||
| 8 | Linear OOA(2219, 1382, F2, 7, 35) (dual of [(1382, 7), 9455, 36]-NRT-code) | [i] | ||
| 9 | Linear OOA(2219, 1382, F2, 8, 35) (dual of [(1382, 8), 10837, 36]-NRT-code) | [i] | ||
| 10 | Digital (184, 219, 1382)-net over F2 | [i] | ||