Information on Result #687002
Linear OA(8133, 32781, F8, 30) (dual of [32781, 32648, 31]-code), using construction XX applied to Ce(29) ⊂ Ce(27) ⊂ Ce(26) based on
- linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(8133, 29180, F8, 2, 30) (dual of [(29180, 2), 58227, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8133, 29180, F8, 3, 30) (dual of [(29180, 3), 87407, 31]-NRT-code) | [i] | ||
| 3 | Digital (103, 133, 29180)-net over F8 | [i] | ||
| 4 | Linear OOA(8133, 16390, F8, 2, 30) (dual of [(16390, 2), 32647, 31]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8133, 10927, F8, 3, 30) (dual of [(10927, 3), 32648, 31]-NRT-code) | [i] | ||