Information on Result #1831990
OOA(3253, 4718591, S32, 2, 9), using (u, u+v)-construction based on
- 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
- OOA(3240, 4194301, S32, 2, 9), using
- OOA 2-folding [i] based on OA(3240, 8388602, S32, 9), using
- discarding factors based on OA(3240, large, S32, 9), using
- discarding parts of the base [i] based on linear OA(6433, large, F64, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding parts of the base [i] based on linear OA(6433, large, F64, 9) (dual of [large, large−33, 10]-code), using
- discarding factors based on OA(3240, large, S32, 9), using
- OOA 2-folding [i] based on OA(3240, 8388602, S32, 9), using
Mode: Constructive.
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 | OOA(3253, 2359295, S32, 10, 9) | [i] | OOA Folding and Stacking with Additional Row | |