Information on Result #698663
Linear OA(6474, 4126, F64, 33) (dual of [4126, 4052, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,11]) based on
- linear OA(6465, 4097, F64, 33) (dual of [4097, 4032, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(6445, 4097, F64, 23) (dual of [4097, 4052, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(649, 29, F64, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,64)), using
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), using
- Reed–Solomon code RS(55,64) [i]
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), using
Mode: Constructive and linear.
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 | OA(3289, 4126, S32, 33) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6474, 3517, F64, 2, 33) (dual of [(3517, 2), 6960, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6474, 3517, F64, 3, 33) (dual of [(3517, 3), 10477, 34]-NRT-code) | [i] | ||
| 4 | Digital (41, 74, 3517)-net over F64 | [i] | ||
| 5 | Linear OOA(6474, 2063, F64, 2, 33) (dual of [(2063, 2), 4052, 34]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6474, 1375, F64, 3, 33) (dual of [(1375, 3), 4051, 34]-NRT-code) | [i] | ||