Information on Result #1822248
OA(12863, 65667, S128, 23), using (u, u+v)-construction based on
- linear OA(12811, 129, F128, 11) (dual of [129, 118, 12]-code or 129-arc in PG(10,128)), using
- extended Reed–Solomon code RSe(118,128) [i]
- the expurgated narrow-sense BCH-code C(I) with length 129 | 1282−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OA(12852, 65538, S128, 23), using
- discarding parts of the base [i] based on linear OA(25645, 65538, F256, 23) (dual of [65538, 65493, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- discarding parts of the base [i] based on linear OA(25645, 65538, F256, 23) (dual of [65538, 65493, 24]-code), using
Mode: Constructive.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | OOA(12863, 32833, S128, 2, 23) | [i] | OOA Folding | |
| 2 | OOA(12863, 21889, S128, 3, 23) | [i] | ||
| 3 | OOA(12863, 5969, S128, 23, 23) | [i] | OOA Folding and Stacking with Additional Row | |