Information on Result #1436688
Linear OOA(552, 390647, F5, 2, 8) (dual of [(390647, 2), 781242, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(552, 390647, F5, 8) (dual of [390647, 390595, 9]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(550, 390643, F5, 8) (dual of [390643, 390593, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(549, 390625, F5, 8) (dual of [390625, 390576, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(517, 18, F5, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,5)), using
- dual of repetition code with length 18 [i]
- linear OA(51, 18, F5, 1) (dual of [18, 17, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(550, 390645, F5, 7) (dual of [390645, 390595, 8]-code), using Gilbert–Varšamov bound and bm = 550 > Vbs−1(k−1) = 20216 193814 027964 445822 360679 409329 [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(550, 390643, F5, 8) (dual of [390643, 390593, 9]-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(552, 195323, F5, 3, 8) (dual of [(195323, 3), 585917, 9]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(552, 195323, F5, 10, 8) (dual of [(195323, 10), 1953178, 9]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |