Information on Result #1452118
Linear OOA(9135, 4783013, F9, 2, 21) (dual of [(4783013, 2), 9565891, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9135, 4783013, F9, 21) (dual of [4783013, 4782878, 22]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9134, 4783011, F9, 21) (dual of [4783011, 4782877, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- linear OA(9127, 4782969, F9, 21) (dual of [4782969, 4782842, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(20) ⊂ Ce(14) [i] based on
- linear OA(9134, 4783012, F9, 20) (dual of [4783012, 4782878, 21]-code), using Gilbert–Varšamov bound and bm = 9134 > Vbs−1(k−1) = 9 725815 668893 396308 554058 987450 248079 828876 814649 438733 656007 537323 208453 805548 006290 436484 224770 811030 949878 294215 263984 206809 [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(9134, 4783011, F9, 21) (dual of [4783011, 4782877, 22]-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(9135, 2391506, F9, 3, 21) (dual of [(2391506, 3), 7174383, 22]-NRT-code) | [i] | OOA Folding | |