Information on Result #1447705
Linear OOA(8156, 2097203, F8, 2, 24) (dual of [(2097203, 2), 4194250, 25]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8156, 2097203, F8, 24) (dual of [2097203, 2097047, 25]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8155, 2097201, F8, 24) (dual of [2097201, 2097046, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(87, 49, F8, 5) (dual of [49, 42, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(8155, 2097202, F8, 23) (dual of [2097202, 2097047, 24]-code), using Gilbert–Varšamov bound and bm = 8155 > Vbs−1(k−1) = 41440 438015 083549 327873 290216 180205 958280 385652 926853 061399 328966 117657 218352 045165 924882 296201 894445 339055 106605 484690 258072 694981 458048 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(8155, 2097201, F8, 24) (dual of [2097201, 2097046, 25]-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(8156, 1048601, F8, 3, 24) (dual of [(1048601, 3), 3145647, 25]-NRT-code) | [i] | OOA Folding | |