Information on Result #1559112
Linear OOA(8169, 2097217, F8, 3, 26) (dual of [(2097217, 3), 6291482, 27]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8169, 2097217, F8, 26) (dual of [2097217, 2097048, 27]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8167, 2097213, F8, 26) (dual of [2097213, 2097046, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(812, 61, F8, 7) (dual of [61, 49, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(812, 73, F8, 7) (dual of [73, 61, 8]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(812, 73, F8, 7) (dual of [73, 61, 8]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(8167, 2097215, F8, 25) (dual of [2097215, 2097048, 26]-code), using Gilbert–Varšamov bound and bm = 8167 > Vbs−1(k−1) = 16181 426395 568563 630130 696101 276865 861966 686197 758110 097464 728105 075110 184768 384377 034430 740845 798779 610639 866227 753017 242339 492133 321170 296336 211969 [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(8167, 2097213, F8, 26) (dual of [2097213, 2097046, 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(8169, 419443, F8, 33, 26) (dual of [(419443, 33), 13841450, 27]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |