Information on Result #1451809
Linear OOA(9129, 4783015, F9, 2, 20) (dual of [(4783015, 2), 9565901, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9129, 4783015, F9, 20) (dual of [4783015, 4782886, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9127, 4783011, F9, 20) (dual of [4783011, 4782884, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(9120, 4782969, F9, 20) (dual of [4782969, 4782849, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(97, 42, F9, 5) (dual of [42, 35, 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(9127, 4783013, F9, 19) (dual of [4783013, 4782886, 20]-code), using Gilbert–Varšamov bound and bm = 9127 > Vbs−1(k−1) = 4 829381 631641 654183 073186 066433 182059 573443 356610 117995 671040 356775 018418 856284 234265 435336 919443 534316 114951 769681 093281 [i]
- linear OA(90, 2, F9, 0) (dual of [2, 2, 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(9127, 4783011, F9, 20) (dual of [4783011, 4782884, 21]-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(9129, 2391507, F9, 3, 20) (dual of [(2391507, 3), 7174392, 21]-NRT-code) | [i] | OOA Folding | |