Information on Result #1068966
Linear OOA(8181, 2098792, F81, 4, 17) (dual of [(2098792, 4), 8395087, 18]-NRT-code), using OOA 2-folding based on linear OOA(8181, 4197584, F81, 2, 17) (dual of [(4197584, 2), 8395087, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8116, 3283, F81, 2, 8) (dual of [(3283, 2), 6550, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8116, 6566, F81, 8) (dual of [6566, 6550, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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(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(7) ⊂ Ce(5) [i] based on
- OOA 2-folding [i] based on linear OA(8116, 6566, F81, 8) (dual of [6566, 6550, 9]-code), using
- linear OOA(8165, 4194301, F81, 2, 17) (dual of [(4194301, 2), 8388537, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8165, 8388602, F81, 17) (dual of [8388602, 8388537, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8165, large, F81, 17) (dual of [large, large−65, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8165, large, F81, 17) (dual of [large, large−65, 18]-code), using
- OOA 2-folding [i] based on linear OA(8165, 8388602, F81, 17) (dual of [8388602, 8388537, 18]-code), using
- linear OOA(8116, 3283, F81, 2, 8) (dual of [(3283, 2), 6550, 9]-NRT-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(8182, 2098792, F81, 4, 17) (dual of [(2098792, 4), 8395086, 18]-NRT-code) | [i] | OOA Duplication | |