Information on Result #686991
Linear OA(8168, 32781, F8, 38) (dual of [32781, 32613, 39]-code), using construction XX applied to Ce(37) ⊂ Ce(35) ⊂ Ce(34) based on
- linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8151, 32768, F8, 35) (dual of [32768, 32617, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(8168, 31526, F8, 2, 38) (dual of [(31526, 2), 62884, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8168, 31526, F8, 3, 38) (dual of [(31526, 3), 94410, 39]-NRT-code) | [i] | ||
| 3 | Digital (130, 168, 31526)-net over F8 | [i] | ||
| 4 | Linear OOA(8168, 16390, F8, 2, 38) (dual of [(16390, 2), 32612, 39]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8168, 10927, F8, 3, 38) (dual of [(10927, 3), 32613, 39]-NRT-code) | [i] | ||