Information on Result #1436905
Linear OOA(562, 390656, F5, 2, 9) (dual of [(390656, 2), 781250, 10]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(562, 390656, F5, 9) (dual of [390656, 390594, 10]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(560, 390652, F5, 9) (dual of [390652, 390592, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(557, 390625, F5, 9) (dual of [390625, 390568, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(53, 27, F5, 2) (dual of [27, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(560, 390654, F5, 8) (dual of [390654, 390594, 9]-code), using Gilbert–Varšamov bound and bm = 560 > Vbs−1(k−1) = 4513 424155 274706 243467 014223 905055 097045 [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(560, 390652, F5, 9) (dual of [390652, 390592, 10]-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(562, 195328, F5, 3, 9) (dual of [(195328, 3), 585922, 10]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(562, 195327, F5, 10, 9) (dual of [(195327, 10), 1953208, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |