Information on Result #687000
Linear OA(8138, 32781, F8, 31) (dual of [32781, 32643, 32]-code), using construction XX applied to Ce(30) ⊂ Ce(28) ⊂ Ce(27) based on
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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(81, 12, F8, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(8138, 30768, F8, 2, 31) (dual of [(30768, 2), 61398, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8138, 30768, F8, 3, 31) (dual of [(30768, 3), 92166, 32]-NRT-code) | [i] | ||
| 3 | Digital (107, 138, 30768)-net over F8 | [i] | ||
| 4 | Linear OOA(8138, 16390, F8, 2, 31) (dual of [(16390, 2), 32642, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8138, 10927, F8, 3, 31) (dual of [(10927, 3), 32643, 32]-NRT-code) | [i] | ||