Information on Result #1561557
Linear OOA(9113, 6578, F9, 3, 31) (dual of [(6578, 3), 19621, 32]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9113, 6578, F9, 31) (dual of [6578, 6465, 32]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9112, 6576, F9, 31) (dual of [6576, 6464, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- linear OA(9109, 6561, F9, 31) (dual of [6561, 6452, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(997, 6561, F9, 28) (dual of [6561, 6464, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(93, 15, F9, 2) (dual of [15, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- linear OA(9112, 6577, F9, 30) (dual of [6577, 6465, 31]-code), using Gilbert–Varšamov bound and bm = 9112 > Vbs−1(k−1) = 8656 684908 192711 126197 785130 684955 422093 514870 924331 053934 796746 499294 556463 215359 061977 838204 526148 196225 [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(9112, 6576, F9, 31) (dual of [6576, 6464, 32]-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(9113, 1315, F9, 33, 31) (dual of [(1315, 33), 43282, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |