Information on Result #1685037
Linear OOA(2199, 699054, F2, 7, 18) (dual of [(699054, 7), 4893179, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2199, 699054, F2, 6, 18) (dual of [(699054, 6), 4194125, 19]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2199, 4194324, F2, 18) (dual of [4194324, 4194125, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2199, 4194327, F2, 18) (dual of [4194327, 4194128, 19]-code), using
- 1 times truncation [i] based on linear OA(2200, 4194328, F2, 19) (dual of [4194328, 4194128, 20]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2199, 4194304, F2, 19) (dual of [4194304, 4194105, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2177, 4194304, F2, 17) (dual of [4194304, 4194127, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(223, 24, F2, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
- dual of repetition code with length 24 [i]
- linear OA(21, 24, F2, 1) (dual of [24, 23, 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 X4 applied to Ce(18) ⊂ Ce(16) [i] based on
- 1 times truncation [i] based on linear OA(2200, 4194328, F2, 19) (dual of [4194328, 4194128, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2199, 4194327, F2, 18) (dual of [4194327, 4194128, 19]-code), using
Mode: 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(2200, 699054, F2, 7, 18) (dual of [(699054, 7), 4893178, 19]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2201, 699054, F2, 7, 18) (dual of [(699054, 7), 4893177, 19]-NRT-code) | [i] | ||