Information on Result #687007
Linear OA(8126, 32789, F8, 28) (dual of [32789, 32663, 29]-code), using construction XX applied to Ce(27) ⊂ Ce(24) ⊂ Ce(22) based on
- linear OA(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8101, 32768, F8, 23) (dual of [32768, 32667, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(83, 19, F8, 2) (dual of [19, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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 OOA(8126, 32789, F8, 2, 28) (dual of [(32789, 2), 65452, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8126, 32789, F8, 3, 28) (dual of [(32789, 3), 98241, 29]-NRT-code) | [i] | ||
| 3 | Digital (98, 126, 32789)-net over F8 | [i] | ||
| 4 | Linear OOA(8126, 2342, F8, 28, 28) (dual of [(2342, 28), 65450, 29]-NRT-code) | [i] | OA Folding and Stacking | |