Information on Result #682471
Linear OA(532, 78142, F5, 6) (dual of [78142, 78110, 7]-code), using construction X applied to Ce(5) ⊂ Ce(2) based on
- linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(515, 78125, F5, 3) (dual of [78125, 78110, 4]-code or 78125-cap in PG(14,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(53, 17, F5, 2) (dual of [17, 14, 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(532, 78142, F5, 2, 6) (dual of [(78142, 2), 156252, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(532, 78142, F5, 3, 6) (dual of [(78142, 3), 234394, 7]-NRT-code) | [i] | ||
| 3 | Digital (26, 32, 78142)-net over F5 | [i] | ||
| 4 | Linear OOA(532, 39071, F5, 2, 6) (dual of [(39071, 2), 78110, 7]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(532, 26047, F5, 3, 6) (dual of [(26047, 3), 78109, 7]-NRT-code) | [i] | ||
| 6 | Linear OOA(532, 26047, F5, 6, 6) (dual of [(26047, 6), 156250, 7]-NRT-code) | [i] | OA Folding and Stacking | |