Information on Result #1721443
Linear OOA(4234, 2348, F4, 45, 42) (dual of [(2348, 45), 105426, 43]-NRT-code), using OOA 7-folding and stacking with additional row based on linear OOA(4234, 16437, F4, 3, 42) (dual of [(16437, 3), 49077, 43]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4234, 16443, F4, 3, 42) (dual of [(16443, 3), 49095, 43]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4234, 16443, F4, 42) (dual of [16443, 16209, 43]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4232, 16440, F4, 42) (dual of [16440, 16208, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(33) [i] based on
- linear OA(4218, 16384, F4, 42) (dual of [16384, 16166, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4176, 16384, F4, 34) (dual of [16384, 16208, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to Ce(41) ⊂ Ce(33) [i] based on
- linear OA(4232, 16441, F4, 40) (dual of [16441, 16209, 41]-code), using Gilbert–Varšamov bound and bm = 4232 > Vbs−1(k−1) = 50011 360254 408330 512553 658232 128297 102883 411717 370148 276172 752057 393406 531559 282848 176511 436705 810054 307638 635487 733972 508690 163093 085621 [i]
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(4232, 16440, F4, 42) (dual of [16440, 16208, 43]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4234, 16443, F4, 42) (dual of [16443, 16209, 43]-code), using
Mode: Linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (192, 234, 2348)-net over F4 | [i] | Net Defined by OOA | |