Information on Result #1436470
Linear OOA(539, 15641, F5, 2, 8) (dual of [(15641, 2), 31243, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(539, 15641, F5, 8) (dual of [15641, 15602, 9]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(538, 15639, F5, 8) (dual of [15639, 15601, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(537, 15625, F5, 8) (dual of [15625, 15588, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(525, 15625, F5, 6) (dual of [15625, 15600, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(513, 14, F5, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,5)), using
- dual of repetition code with length 14 [i]
- linear OA(51, 14, F5, 1) (dual of [14, 13, 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(538, 15640, F5, 7) (dual of [15640, 15602, 8]-code), using Gilbert–Varšamov bound and bm = 538 > Vbs−1(k−1) = 83 158452 840508 053832 593901 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 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(538, 15639, F5, 8) (dual of [15639, 15601, 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(539, 7820, F5, 3, 8) (dual of [(7820, 3), 23421, 9]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(539, 7820, F5, 10, 8) (dual of [(7820, 10), 78161, 9]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |