Information on Result #731213
Linear OA(8122, 524294, F8, 21) (dual of [524294, 524172, 22]-code), using trace code based on linear OA(6461, 262147, F64, 21) (dual of [262147, 262086, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- 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(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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
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 OA(8123, 524295, F8, 21) (dual of [524295, 524172, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8122, 524294, F8, 2, 21) (dual of [(524294, 2), 1048466, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8122, 524294, F8, 3, 21) (dual of [(524294, 3), 1572760, 22]-NRT-code) | [i] | ||
| 4 | Digital (101, 122, 524294)-net over F8 | [i] | ||
| 5 | Linear OA(8123, 524296, F8, 21) (dual of [524296, 524173, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(8122, 262147, F8, 2, 21) (dual of [(262147, 2), 524172, 22]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8122, 174764, F8, 3, 21) (dual of [(174764, 3), 524170, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(8122, 52429, F8, 21, 21) (dual of [(52429, 21), 1100887, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |