Information on Result #1432585
Linear OOA(4234, 16443, F4, 2, 42) (dual of [(16443, 2), 32652, 43]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound 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
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(4234, 8221, F4, 3, 42) (dual of [(8221, 3), 24429, 43]-NRT-code) | [i] | OOA Folding | |