Information on Result #1440174
Linear OOA(5143, 15666, F5, 2, 28) (dual of [(15666, 2), 31189, 29]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5143, 15666, F5, 28) (dual of [15666, 15523, 29]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5142, 15664, F5, 28) (dual of [15664, 15522, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(5133, 15625, F5, 28) (dual of [15625, 15492, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(5103, 15625, F5, 22) (dual of [15625, 15522, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(59, 39, F5, 5) (dual of [39, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(5142, 15665, F5, 27) (dual of [15665, 15523, 28]-code), using Gilbert–Varšamov bound and bm = 5142 > Vbs−1(k−1) = 127 813019 591476 989745 514789 994691 672344 381990 104510 081798 418075 268199 469698 833966 923729 201666 591553 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(5142, 15664, F5, 28) (dual of [15664, 15522, 29]-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(5143, 7833, F5, 3, 28) (dual of [(7833, 3), 23356, 29]-NRT-code) | [i] | OOA Folding | |