Information on Result #1555861
Linear OOA(8114, 32802, F8, 3, 25) (dual of [(32802, 3), 98292, 26]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8114, 32802, F8, 25) (dual of [32802, 32688, 26]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8113, 32800, F8, 25) (dual of [32800, 32687, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(18) [i] based on
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(881, 32768, F8, 19) (dual of [32768, 32687, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(24) ⊂ Ce(18) [i] based on
- linear OA(8113, 32801, F8, 24) (dual of [32801, 32688, 25]-code), using Gilbert–Varšamov bound and bm = 8113 > Vbs−1(k−1) = 77010 824640 495607 895302 842591 674104 238548 485955 522040 762847 240242 416176 920367 164619 338920 386835 360171 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 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(8113, 32800, F8, 25) (dual of [32800, 32687, 26]-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(8114, 8200, F8, 27, 25) (dual of [(8200, 27), 221286, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |