Information on Result #1556231
Linear OOA(8122, 262182, F8, 3, 22) (dual of [(262182, 3), 786424, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8122, 262182, F8, 22) (dual of [262182, 262060, 23]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8121, 262180, F8, 22) (dual of [262180, 262059, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(86, 36, F8, 4) (dual of [36, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(8121, 262181, F8, 21) (dual of [262181, 262060, 22]-code), using Gilbert–Varšamov bound and bm = 8121 > Vbs−1(k−1) = 77182 236898 667585 548992 202771 435062 132605 799388 184683 553553 530828 527529 751500 348397 926774 745079 867640 111608 [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(8121, 262180, F8, 22) (dual of [262180, 262059, 23]-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(8122, 65545, F8, 27, 22) (dual of [(65545, 27), 1769593, 23]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |