Information on Result #1439722
Linear OOA(5135, 78184, F5, 2, 22) (dual of [(78184, 2), 156233, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5135, 78184, F5, 22) (dual of [78184, 78049, 23]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5133, 78180, F5, 22) (dual of [78180, 78047, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(513, 55, F5, 7) (dual of [55, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(513, 63, F5, 7) (dual of [63, 50, 8]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(513, 63, F5, 7) (dual of [63, 50, 8]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(5133, 78182, F5, 21) (dual of [78182, 78049, 22]-code), using Gilbert–Varšamov bound and bm = 5133 > Vbs−1(k−1) = 32 814959 996461 471086 101472 366926 818527 189564 160170 868995 759642 936483 286841 758633 438050 023605 [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(5133, 78180, F5, 22) (dual of [78180, 78047, 23]-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(5135, 39092, F5, 3, 22) (dual of [(39092, 3), 117141, 23]-NRT-code) | [i] | OOA Folding | |