Information on Result #901835
Linear OOA(3251, 4718624, F32, 2, 8) (dual of [(4718624, 2), 9437197, 9]-NRT-code), using (u, u+v)-construction based on
- linear OOA(3215, 524323, F32, 2, 4) (dual of [(524323, 2), 1048631, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(322, 33, F32, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;64,32) [i]
- linear OOA(3213, 524290, F32, 2, 4) (dual of [(524290, 2), 1048567, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3213, 1048580, F32, 4) (dual of [1048580, 1048567, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(3213, 1048576, F32, 4) (dual of [1048576, 1048563, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(329, 1048576, F32, 3) (dual of [1048576, 1048567, 4]-code or 1048576-cap in PG(8,32)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 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(3) ⊂ Ce(2) [i] based on
- OOA 2-folding [i] based on linear OA(3213, 1048580, F32, 4) (dual of [1048580, 1048567, 5]-code), using
- linear OOA(322, 33, F32, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3236, 4194301, F32, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3236, 8388602, F32, 8) (dual of [8388602, 8388566, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, large, F32, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(3236, large, F32, 8) (dual of [large, large−36, 9]-code), using
- OOA 2-folding [i] based on linear OA(3236, 8388602, F32, 8) (dual of [8388602, 8388566, 9]-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(3251, 2359311, F32, 10, 8) (dual of [(2359311, 10), 23593059, 9]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |