Information on Result #698473
Linear OA(6411, 262152, F64, 4) (dual of [262152, 262141, 5]-code), using construction X4 applied to Ce(3) ⊂ Ce(1) based on
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(644, 262144, F64, 2) (dual of [262144, 262140, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(647, 8, F64, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,64)), using
- dual of repetition code with length 8 [i]
- linear OA(641, 8, F64, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), using
- Reed–Solomon code RS(63,64) [i]
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), 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 | Linear OOA(6411, 262152, F64, 2, 4) (dual of [(262152, 2), 524293, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6411, 262152, F64, 3, 4) (dual of [(262152, 3), 786445, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(6411, 131076, F64, 2, 4) (dual of [(131076, 2), 262141, 5]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(6411, 131076, F64, 3, 4) (dual of [(131076, 3), 393217, 5]-NRT-code) | [i] | OA Folding and Stacking | |