Information on Result #1302820
Linear OA(8123, 524296, F8, 21) (dual of [524296, 524173, 22]-code), using construction X with Varšamov bound based on
- linear OA(8122, 524294, F8, 21) (dual of [524294, 524172, 22]-code), using
- trace code [i] 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
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(6461, 262147, F64, 21) (dual of [262147, 262086, 22]-code), using
- linear OA(8122, 524295, F8, 20) (dual of [524295, 524173, 21]-code), using Gilbert–Varšamov bound and bm = 8122 > Vbs−1(k−1) = 440100 240206 448607 498792 836001 080175 872434 311946 680993 171096 544036 275548 479054 611874 954666 715087 871828 099072 [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(8123, 524296, F8, 2, 21) (dual of [(524296, 2), 1048469, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8123, 524296, F8, 3, 21) (dual of [(524296, 3), 1572765, 22]-NRT-code) | [i] | ||
| 3 | Digital (102, 123, 524296)-net over F8 | [i] | ||
| 4 | Linear OOA(8123, 262148, F8, 2, 21) (dual of [(262148, 2), 524173, 22]-NRT-code) | [i] | OOA Folding | |