Information on Result #1463722
Linear OOA(8137, 420173, F81, 2, 12) (dual of [(420173, 2), 840309, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8137, 420173, F81, 12) (dual of [420173, 420136, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, 531456, F81, 12) (dual of [531456, 531419, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(8134, 531441, F81, 12) (dual of [531441, 531407, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(8122, 531441, F81, 8) (dual of [531441, 531419, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(813, 15, F81, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,81) or 15-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
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(8137, 210086, F81, 3, 12) (dual of [(210086, 3), 630221, 13]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8137, 210086, F81, 4, 12) (dual of [(210086, 4), 840307, 13]-NRT-code) | [i] | ||