Information on Result #1445194
Linear OOA(8111, 262183, F8, 2, 20) (dual of [(262183, 2), 524255, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8111, 262183, F8, 20) (dual of [262183, 262072, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8110, 262181, F8, 20) (dual of [262181, 262071, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(8103, 262144, F8, 20) (dual of [262144, 262041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(873, 262144, F8, 14) (dual of [262144, 262071, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(87, 37, F8, 5) (dual of [37, 30, 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(8110, 262182, F8, 19) (dual of [262182, 262072, 20]-code), using Gilbert–Varšamov bound and bm = 8110 > Vbs−1(k−1) = 8 709563 608667 428235 585802 693265 642469 805517 002156 386113 718666 655956 852142 114070 132769 513810 337524 [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(8110, 262181, F8, 20) (dual of [262181, 262071, 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(8111, 131091, F8, 3, 20) (dual of [(131091, 3), 393162, 21]-NRT-code) | [i] | OOA Folding | |