Information on Result #1302843
Linear OA(8129, 524296, F8, 22) (dual of [524296, 524167, 23]-code), using construction X with Varšamov bound based on
- linear OA(8128, 524294, F8, 22) (dual of [524294, 524166, 23]-code), using
- trace code [i] based on linear OA(6464, 262147, F64, 22) (dual of [262147, 262083, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6461, 262144, F64, 21) (dual of [262144, 262083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(6464, 262147, F64, 22) (dual of [262147, 262083, 23]-code), using
- linear OA(8128, 524295, F8, 21) (dual of [524295, 524167, 22]-code), using Gilbert–Varšamov bound and bm = 8128 > Vbs−1(k−1) = 80756 765707 905955 968913 020211 700402 436977 335646 525220 003901 038801 501594 028978 977775 255019 115890 892126 217631 137792 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(8129, 524296, F8, 2, 22) (dual of [(524296, 2), 1048463, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8129, 524296, F8, 3, 22) (dual of [(524296, 3), 1572759, 23]-NRT-code) | [i] | ||
| 3 | Digital (107, 129, 524296)-net over F8 | [i] | ||
| 4 | Linear OOA(8129, 262148, F8, 2, 22) (dual of [(262148, 2), 524167, 23]-NRT-code) | [i] | OOA Folding | |