Information on Result #1016154
Linear OOA(9123, 5596787, F9, 3, 13) (dual of [(5596787, 3), 16790238, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(925, 4385, F9, 3, 6) (dual of [(4385, 3), 13130, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(93, 10, F9, 3, 3) (dual of [(10, 3), 27, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;27,9) [i]
- linear OOA(922, 4375, F9, 3, 6) (dual of [(4375, 3), 13103, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(922, 13125, F9, 6) (dual of [13125, 13103, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(922, 13126, F9, 6) (dual of [13126, 13104, 7]-code), using
- trace code [i] based on linear OA(8111, 6563, F81, 6) (dual of [6563, 6552, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [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(819, 6561, F81, 5) (dual of [6561, 6552, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- trace code [i] based on linear OA(8111, 6563, F81, 6) (dual of [6563, 6552, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(922, 13126, F9, 6) (dual of [13126, 13104, 7]-code), using
- OOA 3-folding [i] based on linear OA(922, 13125, F9, 6) (dual of [13125, 13103, 7]-code), using
- linear OOA(93, 10, F9, 3, 3) (dual of [(10, 3), 27, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- 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(9123, 2798393, F9, 15, 13) (dual of [(2798393, 15), 41975772, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |