Information on Result #1439561
Linear OOA(5132, 390678, F5, 2, 19) (dual of [(390678, 2), 781224, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5132, 390678, F5, 19) (dual of [390678, 390546, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5130, 390674, F5, 19) (dual of [390674, 390544, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(5121, 390625, F5, 19) (dual of [390625, 390504, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(581, 390625, F5, 13) (dual of [390625, 390544, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(59, 49, F5, 5) (dual of [49, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(5130, 390676, F5, 18) (dual of [390676, 390546, 19]-code), using Gilbert–Varšamov bound and bm = 5130 > Vbs−1(k−1) = 5 554825 614034 651205 118533 454904 926096 131402 689202 681077 403773 486084 525966 246882 406970 497341 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(5130, 390674, F5, 19) (dual of [390674, 390544, 20]-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(5132, 195339, F5, 3, 19) (dual of [(195339, 3), 585885, 20]-NRT-code) | [i] | OOA Folding | |