Information on Result #1520418
Linear OOA(343, 59073, F3, 3, 6) (dual of [(59073, 3), 177176, 7]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(343, 59073, F3, 6) (dual of [59073, 59030, 7]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(342, 59071, F3, 6) (dual of [59071, 59029, 7]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(341, 59049, F3, 7) (dual of [59049, 59008, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(321, 59049, F3, 4) (dual of [59049, 59028, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(321, 22, F3, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,3)), using
- dual of repetition code with length 22 [i]
- linear OA(31, 22, F3, 1) (dual of [22, 21, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(342, 59072, F3, 5) (dual of [59072, 59030, 6]-code), using Gilbert–Varšamov bound and bm = 342 > Vbs−1(k−1) = 8 116646 366233 929483 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(342, 59071, F3, 6) (dual of [59071, 59029, 7]-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(343, 59072, F3, 4, 6) (dual of [(59072, 4), 236245, 7]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(343, 59072, F3, 5, 6) (dual of [(59072, 5), 295317, 7]-NRT-code) | [i] | ||