Information on Result #1018614
Linear OOA(8157, 2798389, F81, 3, 12) (dual of [(2798389, 3), 8395110, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8112, 2188, F81, 3, 6) (dual of [(2188, 3), 6552, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8112, 6564, F81, 6) (dual of [6564, 6552, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(8112, 6566, F81, 6) (dual of [6566, 6554, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(8111, 6561, F81, 6) (dual of [6561, 6550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(817, 6561, F81, 4) (dual of [6561, 6554, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(8112, 6566, F81, 6) (dual of [6566, 6554, 7]-code), using
- OOA 3-folding [i] based on linear OA(8112, 6564, F81, 6) (dual of [6564, 6552, 7]-code), using
- linear OOA(8145, 2796201, F81, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(8178, 5594590, F81, 3, 12) (dual of [(5594590, 3), 16783692, 13]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8182, 5596778, F81, 3, 12) (dual of [(5596778, 3), 16790252, 13]-NRT-code) | [i] | ||