Information on Result #1436615
Linear OOA(548, 15650, F5, 2, 9) (dual of [(15650, 2), 31252, 10]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(548, 15650, F5, 9) (dual of [15650, 15602, 10]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(546, 15646, F5, 9) (dual of [15646, 15600, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(543, 15625, F5, 9) (dual of [15625, 15582, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(525, 15625, F5, 6) (dual of [15625, 15600, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(53, 21, F5, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(546, 15648, F5, 8) (dual of [15648, 15602, 9]-code), using Gilbert–Varšamov bound and bm = 546 > Vbs−1(k−1) = 745542 871622 002647 864826 311245 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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(546, 15646, F5, 9) (dual of [15646, 15600, 10]-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(548, 7825, F5, 3, 9) (dual of [(7825, 3), 23427, 10]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(548, 7824, F5, 10, 9) (dual of [(7824, 10), 78192, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |