Information on Result #682292
Linear OA(536, 390644, F5, 6) (dual of [390644, 390608, 7]-code), using construction X applied to Ce(5) ⊂ Ce(2) based on
- linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(517, 390625, F5, 3) (dual of [390625, 390608, 4]-code or 390625-cap in PG(16,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(53, 19, F5, 2) (dual of [19, 16, 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(536, 390644, F5, 2, 6) (dual of [(390644, 2), 781252, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(536, 390644, F5, 3, 6) (dual of [(390644, 3), 1171896, 7]-NRT-code) | [i] | ||
| 3 | Digital (30, 36, 390644)-net over F5 | [i] | ||
| 4 | Linear OOA(536, 195322, F5, 2, 6) (dual of [(195322, 2), 390608, 7]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(536, 130214, F5, 3, 6) (dual of [(130214, 3), 390606, 7]-NRT-code) | [i] | ||
| 6 | Linear OOA(536, 130214, F5, 6, 6) (dual of [(130214, 6), 781248, 7]-NRT-code) | [i] | OA Folding and Stacking | |