Information on Result #1016163
Linear OOA(9134, 7186727, F9, 3, 13) (dual of [(7186727, 3), 21560047, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(936, 1594325, F9, 3, 6) (dual of [(1594325, 3), 4782939, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(936, 4782975, F9, 6) (dual of [4782975, 4782939, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(936, 4782976, F9, 6) (dual of [4782976, 4782940, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(936, 4782969, F9, 6) (dual of [4782969, 4782933, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(929, 4782969, F9, 5) (dual of [4782969, 4782940, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(936, 4782976, F9, 6) (dual of [4782976, 4782940, 7]-code), using
- OOA 3-folding [i] based on linear OA(936, 4782975, F9, 6) (dual of [4782975, 4782939, 7]-code), using
- linear OOA(998, 5592402, F9, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
- trace code [i] based on linear OOA(8149, 2796201, F81, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- trace code [i] based on linear OOA(8149, 2796201, F81, 3, 13) (dual of [(2796201, 3), 8388554, 14]-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(9134, 3593363, F9, 15, 13) (dual of [(3593363, 15), 53900311, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |