Information on Result #682689
Linear OA(5118, 15646, F5, 24) (dual of [15646, 15528, 25]-code), using construction X applied to Ce(23) ⊂ Ce(20) based on
- linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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
Mode: Constructive and 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 OA(5119, 15647, F5, 24) (dual of [15647, 15528, 25]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5118, 11789, F5, 2, 24) (dual of [(11789, 2), 23460, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(5118, 11789, F5, 3, 24) (dual of [(11789, 3), 35249, 25]-NRT-code) | [i] | ||
| 4 | Digital (94, 118, 11789)-net over F5 | [i] | ||
| 5 | Linear OOA(5118, 7823, F5, 2, 24) (dual of [(7823, 2), 15528, 25]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5118, 5215, F5, 3, 24) (dual of [(5215, 3), 15527, 25]-NRT-code) | [i] | ||