Information on Result #1302964
Linear OA(8153, 524296, F8, 26) (dual of [524296, 524143, 27]-code), using construction X with Varšamov bound based on
- linear OA(8152, 524294, F8, 26) (dual of [524294, 524142, 27]-code), using
- trace code [i] based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(25) ⊂ Ce(24) [i] based on
- trace code [i] based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- linear OA(8152, 524295, F8, 25) (dual of [524295, 524143, 26]-code), using Gilbert–Varšamov bound and bm = 8152 > Vbs−1(k−1) = 57 440579 048489 590395 728591 559177 309573 817924 184674 721800 974154 144732 638453 900921 228904 690650 943998 461124 022978 462582 474045 732765 499392 [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(8153, 524296, F8, 2, 26) (dual of [(524296, 2), 1048439, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8153, 524296, F8, 3, 26) (dual of [(524296, 3), 1572735, 27]-NRT-code) | [i] | ||
| 3 | Digital (127, 153, 524296)-net over F8 | [i] | ||
| 4 | Linear OOA(8153, 262148, F8, 2, 26) (dual of [(262148, 2), 524143, 27]-NRT-code) | [i] | OOA Folding | |