Information on Result #1302737
Linear OA(8111, 524296, F8, 19) (dual of [524296, 524185, 20]-code), using construction X with Varšamov bound based on
- linear OA(8110, 524294, F8, 19) (dual of [524294, 524184, 20]-code), using
- trace code [i] based on linear OA(6455, 262147, F64, 19) (dual of [262147, 262092, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(18) ⊂ Ce(17) [i] based on
- trace code [i] based on linear OA(6455, 262147, F64, 19) (dual of [262147, 262092, 20]-code), using
- linear OA(8110, 524295, F8, 18) (dual of [524295, 524185, 19]-code), using Gilbert–Varšamov bound and bm = 8110 > Vbs−1(k−1) = 11 175336 576496 700365 290371 242454 314283 012677 675582 594754 438476 389156 054738 904322 563758 966076 899328 [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(8111, 524296, F8, 2, 19) (dual of [(524296, 2), 1048481, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8111, 524296, F8, 3, 19) (dual of [(524296, 3), 1572777, 20]-NRT-code) | [i] | ||
| 3 | Digital (92, 111, 524296)-net over F8 | [i] | ||
| 4 | Linear OOA(8111, 262148, F8, 2, 19) (dual of [(262148, 2), 524185, 20]-NRT-code) | [i] | OOA Folding | |