Information on Result #1451282
Linear OOA(9118, 4783003, F9, 2, 18) (dual of [(4783003, 2), 9565888, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9118, 4783003, F9, 18) (dual of [4783003, 4782885, 19]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9117, 4783001, F9, 18) (dual of [4783001, 4782884, 19]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(9117, 4783002, F9, 17) (dual of [4783002, 4782885, 18]-code), using Gilbert–Varšamov bound and bm = 9117 > Vbs−1(k−1) = 1 009292 463814 366584 286158 708107 182248 611649 524185 002343 876765 173304 388577 561308 203842 006942 323565 812557 656009 [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(9117, 4783001, F9, 18) (dual of [4783001, 4782884, 19]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(9118, 2391501, F9, 3, 18) (dual of [(2391501, 3), 7174385, 19]-NRT-code) | [i] | OOA Folding | |