Information on Result #1445597
Linear OOA(8120, 32804, F8, 2, 26) (dual of [(32804, 2), 65488, 27]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8120, 32804, F8, 26) (dual of [32804, 32684, 27]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8118, 32800, F8, 26) (dual of [32800, 32682, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(886, 32768, F8, 20) (dual of [32768, 32682, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(8118, 32802, F8, 25) (dual of [32802, 32684, 26]-code), using Gilbert–Varšamov bound and bm = 8118 > Vbs−1(k−1) = 736 762561 909082 604393 811800 266375 984523 760238 003475 094296 858920 330895 985895 776870 511027 824062 597701 751668 [i]
- linear OA(80, 2, F8, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(8118, 32800, F8, 26) (dual of [32800, 32682, 27]-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(8120, 16402, F8, 3, 26) (dual of [(16402, 3), 49086, 27]-NRT-code) | [i] | OOA Folding | |