Information on Result #1446003
Linear OOA(8128, 2097196, F8, 2, 20) (dual of [(2097196, 2), 4194264, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8128, 2097196, F8, 20) (dual of [2097196, 2097068, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8127, 2097194, F8, 20) (dual of [2097194, 2097067, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(87, 42, F8, 5) (dual of [42, 35, 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(19) ⊂ Ce(13) [i] based on
- linear OA(8127, 2097195, F8, 19) (dual of [2097195, 2097068, 20]-code), using Gilbert–Varšamov bound and bm = 8127 > Vbs−1(k−1) = 156634 514891 273957 503802 387268 063775 593707 471630 844215 705938 065895 684753 181573 327013 377299 903284 470260 788666 155224 [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(8127, 2097194, F8, 20) (dual of [2097194, 2097067, 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(8128, 1048598, F8, 3, 20) (dual of [(1048598, 3), 3145666, 21]-NRT-code) | [i] | OOA Folding | |