Information on Result #686430
Linear OA(8170, 262151, F8, 33) (dual of [262151, 261981, 34]-code), using construction X applied to Ce(32) ⊂ Ce(30) based on
- linear OA(8169, 262144, F8, 33) (dual of [262144, 261975, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8163, 262144, F8, 31) (dual of [262144, 261981, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(81, 7, F8, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-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(8169, 262150, F8, 32) (dual of [262150, 261981, 33]-code) | [i] | Truncation | |
| 2 | Linear OOA(8170, 148654, F8, 2, 33) (dual of [(148654, 2), 297138, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8170, 148654, F8, 3, 33) (dual of [(148654, 3), 445792, 34]-NRT-code) | [i] | ||
| 4 | Digital (137, 170, 148654)-net over F8 | [i] | ||
| 5 | Linear OOA(8170, 131075, F8, 2, 33) (dual of [(131075, 2), 261980, 34]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8170, 87383, F8, 3, 33) (dual of [(87383, 3), 261979, 34]-NRT-code) | [i] | ||