Information on Result #902153
Linear OOA(32107, 4210719, F32, 2, 17) (dual of [(4210719, 2), 8421331, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(3226, 16418, F32, 2, 8) (dual of [(16418, 2), 32810, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(324, 33, F32, 2, 4) (dual of [(33, 2), 62, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;62,32) [i]
- linear OOA(3222, 16385, F32, 2, 8) (dual of [(16385, 2), 32748, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3222, 32770, F32, 8) (dual of [32770, 32748, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3222, 32771, F32, 8) (dual of [32771, 32749, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(3219, 32768, F32, 7) (dual of [32768, 32749, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(3222, 32771, F32, 8) (dual of [32771, 32749, 9]-code), using
- OOA 2-folding [i] based on linear OA(3222, 32770, F32, 8) (dual of [32770, 32748, 9]-code), using
- linear OOA(324, 33, F32, 2, 4) (dual of [(33, 2), 62, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3281, 4194301, F32, 2, 17) (dual of [(4194301, 2), 8388521, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3281, 8388602, F32, 17) (dual of [8388602, 8388521, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3281, large, F32, 17) (dual of [large, large−81, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, 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(3281, large, F32, 17) (dual of [large, large−81, 18]-code), using
- OOA 2-folding [i] based on linear OA(3281, 8388602, F32, 17) (dual of [8388602, 8388521, 18]-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(32107, 1052679, F32, 18, 17) (dual of [(1052679, 18), 18948115, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |