Information on Result #1832161
OOA(32109, 5242878, S32, 2, 17), using (u, u+v)-construction based on
- OOA(3231, 1048577, S32, 2, 8), using
- OOA 2-folding [i] based on OA(3231, 2097154, S32, 8), using
- discarding factors based on OA(3231, 2097155, S32, 8), using
- discarding parts of the base [i] based on linear OA(12822, 2097155, F128, 8) (dual of [2097155, 2097133, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding parts of the base [i] based on linear OA(12822, 2097155, F128, 8) (dual of [2097155, 2097133, 9]-code), using
- discarding factors based on OA(3231, 2097155, S32, 8), using
- OOA 2-folding [i] based on OA(3231, 2097154, S32, 8), using
- OOA(3278, 4194301, S32, 2, 17), using
- OOA 2-folding [i] based on OA(3278, 8388602, S32, 17), using
- discarding factors based on OA(3278, large, S32, 17), using
- discarding parts of the base [i] based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding parts of the base [i] based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- discarding factors based on OA(3278, large, S32, 17), using
- OOA 2-folding [i] based on OA(3278, 8388602, S32, 17), 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(32109, 1310719, S32, 18, 17) | [i] | OOA Folding and Stacking with Additional Row | |