Information on Result #682671
Linear OA(582, 15640, F5, 17) (dual of [15640, 15558, 18]-code), using construction X applied to Ce(16) ⊂ Ce(13) based on
- linear OA(579, 15625, F5, 17) (dual of [15625, 15546, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(53, 15, F5, 2) (dual of [15, 12, 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 OOA(582, 9543, F5, 2, 17) (dual of [(9543, 2), 19004, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(582, 9543, F5, 3, 17) (dual of [(9543, 3), 28547, 18]-NRT-code) | [i] | ||
| 3 | Digital (65, 82, 9543)-net over F5 | [i] | ||
| 4 | Linear OOA(582, 7820, F5, 2, 17) (dual of [(7820, 2), 15558, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(582, 5213, F5, 3, 17) (dual of [(5213, 3), 15557, 18]-NRT-code) | [i] | ||