Information on Result #1422092
Linear OOA(4117, 16432, F4, 2, 20) (dual of [(16432, 2), 32747, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4117, 16432, F4, 20) (dual of [16432, 16315, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4115, 16428, F4, 20) (dual of [16428, 16313, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(471, 16384, F4, 14) (dual of [16384, 16313, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(49, 44, F4, 5) (dual of [44, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(4115, 16430, F4, 19) (dual of [16430, 16315, 20]-code), using Gilbert–Varšamov bound and bm = 4115 > Vbs−1(k−1) = 455 989414 455769 880654 868629 179854 757595 121687 161414 594478 465771 219916 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(4115, 16428, F4, 20) (dual of [16428, 16313, 21]-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(4117, 8216, F4, 3, 20) (dual of [(8216, 3), 24531, 21]-NRT-code) | [i] | OOA Folding | |