Information on Result #687014
Linear OA(898, 32781, F8, 22) (dual of [32781, 32683, 23]-code), using construction XX applied to Ce(21) ⊂ Ce(19) ⊂ Ce(18) based on
- linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(886, 32768, F8, 20) (dual of [32768, 32682, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(881, 32768, F8, 19) (dual of [32768, 32687, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(898, 28446, F8, 2, 22) (dual of [(28446, 2), 56794, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(898, 28446, F8, 3, 22) (dual of [(28446, 3), 85240, 23]-NRT-code) | [i] | ||
| 3 | Digital (76, 98, 28446)-net over F8 | [i] | ||
| 4 | Linear OOA(898, 16390, F8, 2, 22) (dual of [(16390, 2), 32682, 23]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(898, 10927, F8, 3, 22) (dual of [(10927, 3), 32683, 23]-NRT-code) | [i] | ||
| 6 | Linear OOA(898, 2980, F8, 22, 22) (dual of [(2980, 22), 65462, 23]-NRT-code) | [i] | OA Folding and Stacking | |