Information on Result #1539609
Linear OOA(4177, 16442, F4, 3, 31) (dual of [(16442, 3), 49149, 32]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4177, 16442, F4, 31) (dual of [16442, 16265, 32]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4176, 16440, F4, 31) (dual of [16440, 16264, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(22) [i] based on
- linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to Ce(30) ⊂ Ce(22) [i] based on
- linear OA(4176, 16441, F4, 30) (dual of [16441, 16265, 31]-code), using Gilbert–Varšamov bound and bm = 4176 > Vbs−1(k−1) = 1382 466253 190924 163828 118526 786517 027729 241747 118198 040792 321081 103193 507061 702150 618821 241794 685777 368860 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 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(4176, 16440, F4, 31) (dual of [16440, 16264, 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(4177, 3288, F4, 33, 31) (dual of [(3288, 33), 108327, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |