Information on Result #1450336
Linear OOA(994, 59083, F9, 2, 20) (dual of [(59083, 2), 118072, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(994, 59083, F9, 20) (dual of [59083, 58989, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(993, 59081, F9, 20) (dual of [59081, 58988, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(986, 59049, F9, 20) (dual of [59049, 58963, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(961, 59049, F9, 14) (dual of [59049, 58988, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(97, 32, F9, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(993, 59082, F9, 19) (dual of [59082, 58989, 20]-code), using Gilbert–Varšamov bound and bm = 993 > Vbs−1(k−1) = 215 889528 241362 980167 966869 989370 080376 446716 036631 951717 547879 540453 103251 481741 614921 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(993, 59081, F9, 20) (dual of [59081, 58988, 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(994, 29541, F9, 3, 20) (dual of [(29541, 3), 88529, 21]-NRT-code) | [i] | OOA Folding | |