Information on Result #682470
Linear OA(539, 78142, F5, 7) (dual of [78142, 78103, 8]-code), using construction X applied to Ce(6) ⊂ Ce(3) based on
- linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(522, 78125, F5, 4) (dual of [78125, 78103, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(539, 78142, F5, 2, 7) (dual of [(78142, 2), 156245, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(539, 78142, F5, 3, 7) (dual of [(78142, 3), 234387, 8]-NRT-code) | [i] | ||
| 3 | Digital (32, 39, 78142)-net over F5 | [i] | ||
| 4 | Linear OOA(539, 39071, F5, 2, 7) (dual of [(39071, 2), 78103, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(539, 26047, F5, 3, 7) (dual of [(26047, 3), 78102, 8]-NRT-code) | [i] | ||