Information on Result #1549787
Linear OOA(5124, 78173, F5, 3, 20) (dual of [(78173, 3), 234395, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5124, 78173, F5, 20) (dual of [78173, 78049, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5122, 78169, F5, 20) (dual of [78169, 78047, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(5122, 78171, F5, 19) (dual of [78171, 78049, 20]-code), using Gilbert–Varšamov bound and bm = 5122 > Vbs−1(k−1) = 127243 541995 582269 712602 769755 424076 618807 471408 522340 486071 431031 453451 727584 655289 [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(5122, 78169, F5, 20) (dual of [78169, 78047, 21]-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(5124, 19543, F5, 27, 20) (dual of [(19543, 27), 527537, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |