Information on Result #1448811
Linear OOA(8171, 262189, F8, 2, 31) (dual of [(262189, 2), 524207, 32]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8171, 262189, F8, 31) (dual of [262189, 262018, 32]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8170, 262187, F8, 31) (dual of [262187, 262017, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(8163, 262144, F8, 31) (dual of [262144, 261981, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(87, 43, F8, 5) (dual of [43, 36, 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(30) ⊂ Ce(24) [i] based on
- linear OA(8170, 262188, F8, 30) (dual of [262188, 262018, 31]-code), using Gilbert–Varšamov bound and bm = 8170 > Vbs−1(k−1) = 5 016053 302511 758921 702350 391057 937969 847287 785423 947670 100842 644658 467119 400216 906883 982337 068539 506507 935193 883039 772859 548614 666015 358020 869510 772912 [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(8170, 262187, F8, 31) (dual of [262187, 262017, 32]-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(8171, 131094, F8, 3, 31) (dual of [(131094, 3), 393111, 32]-NRT-code) | [i] | OOA Folding | |