Information on Result #682462
Linear OA(567, 78142, F5, 12) (dual of [78142, 78075, 13]-code), using construction X applied to Ce(11) ⊂ Ce(8) based on
- linear OA(564, 78125, F5, 12) (dual of [78125, 78061, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(567, 46458, F5, 2, 12) (dual of [(46458, 2), 92849, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(567, 46458, F5, 3, 12) (dual of [(46458, 3), 139307, 13]-NRT-code) | [i] | ||
| 3 | Digital (55, 67, 46458)-net over F5 | [i] | ||
| 4 | Linear OOA(567, 39071, F5, 2, 12) (dual of [(39071, 2), 78075, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(567, 26047, F5, 3, 12) (dual of [(26047, 3), 78074, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(567, 13023, F5, 12, 12) (dual of [(13023, 12), 156209, 13]-NRT-code) | [i] | OA Folding and Stacking | |