Information on Result #901973
Linear OOA(3280, 4210719, F32, 2, 13) (dual of [(4210719, 2), 8421358, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(3219, 16418, F32, 2, 6) (dual of [(16418, 2), 32817, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(323, 33, F32, 2, 3) (dual of [(33, 2), 63, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;63,32) [i]
- linear OOA(3216, 16385, F32, 2, 6) (dual of [(16385, 2), 32754, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3216, 32770, F32, 6) (dual of [32770, 32754, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(3216, 32771, F32, 6) (dual of [32771, 32755, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(3216, 32768, F32, 6) (dual of [32768, 32752, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3213, 32768, F32, 5) (dual of [32768, 32755, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(3216, 32771, F32, 6) (dual of [32771, 32755, 7]-code), using
- OOA 2-folding [i] based on linear OA(3216, 32770, F32, 6) (dual of [32770, 32754, 7]-code), using
- linear OOA(323, 33, F32, 2, 3) (dual of [(33, 2), 63, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3261, 4194301, F32, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3261, 8388602, F32, 13) (dual of [8388602, 8388541, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- OOA 2-folding [i] based on linear OA(3261, 8388602, F32, 13) (dual of [8388602, 8388541, 14]-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(3280, 1403572, F32, 14, 13) (dual of [(1403572, 14), 19649928, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |