Information on Result #689246
Linear OA(9117, 531456, F9, 22) (dual of [531456, 531339, 23]-code), using construction XX applied to Ce(21) ⊂ Ce(19) ⊂ Ce(18) based on
- linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(9103, 531441, F9, 20) (dual of [531441, 531338, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(91, 14, F9, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- linear OA(90, 1, F9, 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(9117, 355475, F9, 2, 22) (dual of [(355475, 2), 710833, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9117, 355475, F9, 3, 22) (dual of [(355475, 3), 1066308, 23]-NRT-code) | [i] | ||
| 3 | Digital (95, 117, 355475)-net over F9 | [i] | ||
| 4 | Linear OOA(9117, 265728, F9, 2, 22) (dual of [(265728, 2), 531339, 23]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(9117, 177152, F9, 3, 22) (dual of [(177152, 3), 531339, 23]-NRT-code) | [i] | ||